{"id":620676,"date":"2026-11-09T09:29:28","date_gmt":"2026-11-09T02:29:28","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=620676"},"modified":"2026-11-09T09:35:59","modified_gmt":"2026-11-09T02:35:59","slug":"khoang-cach-tu-diem-den-duong-thang","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/khoang-cach-tu-diem-den-duong-thang\/","title":{"rendered":"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: C\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"<p style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/b><span style=\"font-weight: 400;\"> l\u00e0 \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb \u0111i\u1ec3m \u0111\u00f3 \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng. Trong m\u1eb7t ph\u1eb3ng Oxy, v\u1edbi \u0111i\u1ec3m M(x\u2080; y\u2080) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0394: ax + by + c = 0, c\u00f4ng th\u1ee9c l\u00e0 d(M, \u0394) = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2). C\u00f4ng th\u1ee9c n\u00e0y th\u01b0\u1eddng g\u1eb7p trong To\u00e1n l\u1edbp 10 v\u00e0 l\u1edbp 12, t\u1eeb b\u00e0i t\u1eadp c\u01a1 b\u1ea3n \u0111\u1ebfn b\u00e0i h\u00ecnh h\u1ecdc t\u1ecda \u0111\u1ed9 n\u00e2ng cao. B\u00e0i vi\u1ebft t\u1ed5ng h\u1ee3p c\u00f4ng th\u1ee9c trong m\u1eb7t ph\u1eb3ng Oxy, trong kh\u00f4ng gian Oxyz, kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng song song, kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn m\u1eb7t ph\u1eb3ng v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 g\u00ec?<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Cho \u0111i\u1ec3m M v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0394. G\u1ecdi H l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a M l\u00ean \u0394 (MH \u22a5 \u0394, H \u2208 \u0394). Khi \u0111\u00f3 \u0111\u1ed9 d\u00e0i MH \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn \u0394, k\u00fd hi\u1ec7u d(M, \u0394).<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">MH l\u00e0 \u0111o\u1ea1n ng\u1eafn nh\u1ea5t trong m\u1ecdi \u0111o\u1ea1n n\u1ed1i M v\u1edbi m\u1ed9t \u0111i\u1ec3m tr\u00ean \u0394.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu M n\u1eb1m tr\u00ean \u0394 th\u00ec d(M, \u0394) = 0.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Trong h\u00ecnh h\u1ecdc ph\u1eb3ng kh\u00f4ng c\u00f3 t\u1ecda \u0111\u1ed9, ta th\u01b0\u1eddng t\u00ednh MH b\u1eb1ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng ho\u1eb7c<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dinh-ly-pytago\/\"> <span style=\"font-weight: 400;\">\u0111\u1ecbnh l\u00fd Pytago<\/span><\/a><span style=\"font-weight: 400;\">. Khi c\u00f3 h\u1ec7 t\u1ecda \u0111\u1ed9, ta d\u00f9ng c\u00f4ng th\u1ee9c \u0111\u1ea1i s\u1ed1 d\u01b0\u1edbi \u0111\u00e2y.\u00a0<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-622358\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-4.jpg\" alt=\"khoang-cach-tu-diem-den-duong-thang-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>C\u00f4ng th\u1ee9c t\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng trong Oxy<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Cho \u0111i\u1ec3m M(x\u2080; y\u2080) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0394 c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t ax + by + c = 0 (a\u00b2 + b\u00b2 \u2260 0). Kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn \u0394 l\u00e0:<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">d(M, \u0394) = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00e1ch nh\u1edb: thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m v\u00e0o v\u1ebf tr\u00e1i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng, l\u1ea5y tr\u1ecb tuy\u1ec7t \u0111\u1ed1i, r\u1ed3i chia cho \u0111\u1ed9 d\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/vecto-phap-tuyen\/\">vect\u01a1 ph\u00e1p tuy\u1ebfn<\/a> n\u2192 = (a; b).<\/span><\/p>\n<p style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 1<\/b><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb M(1; 2) \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0394: 3x + 4y \u2212 1 = 0.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d(M, \u0394) = |3\u00b71 + 4\u00b72 \u2212 1| \/ \u221a(3\u00b2 + 4\u00b2) = |10| \/ 5 = 2.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 2<\/b><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb M(\u22122; 3) \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0394: x \u2212 2y + 3 = 0.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d(M, \u0394) = |\u22122 \u2212 6 + 3| \/ \u221a(1 + 4) = 5\/\u221a5 = \u221a5.<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>\u0110\u01b0\u1eddng th\u1eb3ng cho \u1edf d\u1ea1ng tham s\u1ed1 th\u00ec t\u00ednh th\u1ebf n\u00e0o?<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh <\/span><b>kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/b><span style=\"font-weight: 400;\"> tr\u00ean ch\u1ec9 d\u00f9ng \u0111\u01b0\u1ee3c khi \u0111\u01b0\u1eddng th\u1eb3ng \u1edf d\u1ea1ng t\u1ed5ng qu\u00e1t. N\u1ebfu \u0111\u1ec1 cho ph\u01b0\u01a1ng tr\u00ecnh tham s\u1ed1 ho\u1eb7c ch\u00ednh t\u1eafc, b\u1ea1n c\u1ea7n chuy\u1ec3n v\u1ec1 d\u1ea1ng t\u1ed5ng qu\u00e1t tr\u01b0\u1edbc.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh tham s\u1ed1 x = x\u2081 + u\u2081t, y = y\u2081 + u\u2082t, l\u1ea5y vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng u\u2192 = (u\u2081; u\u2082).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Suy ra vect\u01a1 ph\u00e1p tuy\u1ebfn n\u2192 = (u\u2082; \u2212u\u2081).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t: u\u2082(x \u2212 x\u2081) \u2212 u\u2081(y \u2212 y\u2081) = 0.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 3: T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb g\u1ed1c t\u1ecda \u0111\u1ed9 O \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng d: x = 1 + 2t, y = \u22121 + t.<\/b><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">u\u2192 = (2; 1) n\u00ean n\u2192 = (1; \u22122); d \u0111i qua (1; \u22121).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t: (x \u2212 1) \u2212 2(y + 1) = 0 \u21d4 x \u2212 2y \u2212 3 = 0.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d(O, d) = |0 \u2212 0 \u2212 3| \/ \u221a5 = 3\/\u221a5 = 3\u221a5\/5.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00e1ch chuy\u1ec3n \u0111\u1ed5i gi\u1eefa c\u00e1c d\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y chi ti\u1ebft trong b\u00e0i<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-duong-thang\/\"> <span style=\"font-weight: 400;\">ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng<\/span><\/a><span style=\"font-weight: 400;\">.\u00a0<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-622357\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-3.jpg\" alt=\"khoang-cach-tu-diem-den-duong-thang-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng song song<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Hai \u0111\u01b0\u1eddng th\u1eb3ng song song \u0394\u2081: ax + by + c\u2081 = 0 v\u00e0 \u0394\u2082: ax + by + c\u2082 = 0 (c\u00f9ng h\u1ec7 s\u1ed1 a, b) c\u00e1ch nhau:<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">d(\u0394\u2081, \u0394\u2082) = |c\u2081 \u2212 c\u2082| \/ \u221a(a\u00b2 + b\u00b2)<\/span><\/p>\n<p style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 4: T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa \u0394\u2081: 3x + 4y \u2212 1 = 0 v\u00e0 \u0394\u2082: 3x + 4y + 9 = 0.<\/b><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d = |\u22121 \u2212 9| \/ 5 = 10\/5 = 2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">L\u01b0u \u00fd: n\u1ebfu hai ph\u01b0\u01a1ng tr\u00ecnh ch\u01b0a c\u00f9ng h\u1ec7 s\u1ed1 a, b (v\u00ed d\u1ee5 3x + 4y \u2212 1 = 0 v\u00e0 6x + 8y + 18 = 0), h\u00e3y chia ho\u1eb7c nh\u00e2n \u0111\u1ec3 \u0111\u01b0a v\u1ec1 c\u00f9ng h\u1ec7 s\u1ed1 tr\u01b0\u1edbc khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c.<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-622356\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-2.jpg\" alt=\"khoang-cach-tu-diem-den-duong-thang-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng trong kh\u00f4ng gian Oxyz<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Trong kh\u00f4ng gian, \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t d\u1ea1ng ax + by + c = 0, n\u00ean ta d\u00f9ng t\u00edch c\u00f3 h\u01b0\u1edbng. Cho \u0111\u01b0\u1eddng th\u1eb3ng \u0394 \u0111i qua \u0111i\u1ec3m A, c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng u\u2192, v\u00e0 \u0111i\u1ec3m M b\u1ea5t k\u1ef3:<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">d(M, \u0394) = |[AM\u2192, u\u2192]| \/ |u\u2192|<\/span><\/p>\n<p style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 5:\u00a0<\/b><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng th\u1eb3ng \u0394 \u0111i qua A(1; 0; 0), c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng u\u2192 = (1; 1; 0). T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb M(0; 1; 1) \u0111\u1ebfn \u0394.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">AM\u2192 = (\u22121; 1; 1).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">[AM\u2192, u\u2192] = (1\u00b70 \u2212 1\u00b71; 1\u00b71 \u2212 (\u22121)\u00b70; (\u22121)\u00b71 \u2212 1\u00b71) = (\u22121; 1; \u22122), c\u00f3 \u0111\u1ed9 d\u00e0i \u221a6.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">|u\u2192| = \u221a2, suy ra d(M, \u0394) = \u221a6\/\u221a2 = \u221a3.<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn m\u1eb7t ph\u1eb3ng v\u00e0 gi\u1eefa hai m\u1eb7t ph\u1eb3ng<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">\u0110\u00e2y l\u00e0 ph\u1ea7n m\u1edf r\u1ed9ng th\u01b0\u1eddng \u0111i k\u00e8m trong ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 12 \u1edf b\u00e0i h\u1ecdc v\u1ec1 <\/span><b>kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/b><span style=\"font-weight: 400;\">. Cho \u0111i\u1ec3m M(x\u2080; y\u2080; z\u2080) v\u00e0 m\u1eb7t ph\u1eb3ng (P): Ax + By + Cz + D = 0:<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">d(M, (P)) = |Ax\u2080 + By\u2080 + Cz\u2080 + D| \/ \u221a(A\u00b2 + B\u00b2 + C\u00b2)<\/span><\/p>\n<p style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 6:\u00a0<\/b><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb M(1; \u22122; 3) \u0111\u1ebfn (P): 2x \u2212 y + 2z \u2212 1 = 0.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d = |2 + 2 + 6 \u2212 1| \/ \u221a(4 + 1 + 4) = 9\/3 = 3.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Hai m\u1eb7t ph\u1eb3ng song song (P): Ax + By + Cz + D\u2081 = 0 v\u00e0 (Q): Ax + By + Cz + D\u2082 = 0 c\u00e1ch nhau |D\u2081 \u2212 D\u2082| \/ \u221a(A\u00b2 + B\u00b2 + C\u00b2). V\u00ed d\u1ee5, 2x \u2212 y + 2z \u2212 1 = 0 v\u00e0 2x \u2212 y + 2z + 5 = 0 c\u00e1ch nhau 6\/3 = 2. Xem th\u00eam c\u00e1ch l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh trong b\u00e0i<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-mat-phang\/\"> <span style=\"font-weight: 400;\">ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng<\/span><\/a><span style=\"font-weight: 400;\">.\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-622355\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-1.jpg\" alt=\"khoang-cach-tu-diem-den-duong-thang-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>B\u1ea3ng t\u1ed5ng h\u1ee3p c\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00e1c c\u00f4ng th\u1ee9c t\u00ednh kho\u1ea3ng c\u00e1ch trong h\u00ecnh h\u1ecdc th\u01b0\u1eddng xu\u1ea5t hi\u1ec7n \u1edf nhi\u1ec1u d\u1ea1ng b\u00e0i t\u1eadp kh\u00e1c nhau, t\u1eeb h\u00ecnh h\u1ecdc ph\u1eb3ng \u0111\u1ebfn h\u00ecnh h\u1ecdc kh\u00f4ng gian. Vi\u1ec7c h\u1ec7 th\u1ed1ng h\u00f3a c\u00e1c c\u00f4ng th\u1ee9c th\u00e0nh b\u1ea3ng t\u1ed5ng h\u1ee3p s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 tra c\u1ee9u, ghi nh\u1edb v\u00e0 l\u1ef1a ch\u1ecdn c\u00e1ch t\u00ednh ph\u00f9 h\u1ee3p khi gi\u1ea3i to\u00e1n.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Tr\u01b0\u1eddng h\u1ee3p<\/b><\/td>\n<td><b>C\u00f4ng th\u1ee9c<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">\u0110i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng (Oxy)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">|ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Hai \u0111\u01b0\u1eddng th\u1eb3ng song song (Oxy)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">|c\u2081 \u2212 c\u2082| \/ \u221a(a\u00b2 + b\u00b2)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">\u0110i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng (Oxyz)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">|[AM\u2192, u\u2192]| \/ |u\u2192|<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">\u0110i\u1ec3m \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (Oxyz)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">|Ax\u2080 + By\u2080 + Cz\u2080 + D| \/ \u221a(A\u00b2 + B\u00b2 + C\u00b2)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Hai m\u1eb7t ph\u1eb3ng song song (Oxyz)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">|D\u2081 \u2212 D\u2082| \/ \u221a(A\u00b2 + B\u00b2 + C\u00b2)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: justify;\"><b>L\u1ed7i th\u01b0\u1eddng g\u1eb7p khi t\u00ednh kho\u1ea3ng c\u00e1ch<\/b><\/h2>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Qu\u00ean tr\u1ecb tuy\u1ec7t \u0111\u1ed1i:<\/b><span style=\"font-weight: 400;\"> kho\u1ea3ng c\u00e1ch lu\u00f4n kh\u00f4ng \u00e2m; \u1edf V\u00ed d\u1ee5 2, t\u1eed s\u1ed1 l\u00e0 \u22125 nh\u01b0ng ph\u1ea3i l\u1ea5y |\u22125| = 5.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>D\u00f9ng ph\u01b0\u01a1ng tr\u00ecnh tham s\u1ed1 tr\u1ef1c ti\u1ebfp:<\/b><span style=\"font-weight: 400;\"> ph\u1ea3i \u0111\u1ed5i v\u1ec1 d\u1ea1ng t\u1ed5ng qu\u00e1t tr\u01b0\u1edbc.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Qu\u00ean c\u0103n \u1edf m\u1eabu:<\/b><span style=\"font-weight: 400;\"> m\u1eabu l\u00e0 \u221a(a\u00b2 + b\u00b2), kh\u00f4ng ph\u1ea3i a\u00b2 + b\u00b2. N\u1ebfu ch\u01b0a ch\u1eafc ph\u1ea7n c\u0103n th\u1ee9c, b\u1ea1n c\u00f3 th\u1ec3 \u00f4n l\u1ea1i<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/can-bac-hai-la-gi\/\"> <span style=\"font-weight: 400;\">c\u0103n b\u1eadc hai<\/span><\/a><span style=\"font-weight: 400;\">.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Hai \u0111\u01b0\u1eddng song song ch\u01b0a c\u00f9ng h\u1ec7 s\u1ed1:<\/b><span style=\"font-weight: 400;\"> ph\u1ea3i quy v\u1ec1 c\u00f9ng a, b m\u1edbi \u0111\u01b0\u1ee3c tr\u1eeb c\u2081 \u2212 c\u2082.<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/b><\/h2>\n<h3 style=\"text-align: justify;\"><b>C\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch t\u1eeb 1 \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 g\u00ec?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">V\u1edbi \u0111i\u1ec3m M(x\u2080; y\u2080) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng ax + by + c = 0, kho\u1ea3ng c\u00e1ch l\u00e0 d = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2).<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng h\u1ecdc \u1edf l\u1edbp m\u1ea5y?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 10; c\u00f4ng th\u1ee9c trong kh\u00f4ng gian Oxyz \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 12.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 \u00e2m kh\u00f4ng?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Kh\u00f4ng. Kho\u1ea3ng c\u00e1ch lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0, v\u00ec v\u1eady c\u00f4ng th\u1ee9c c\u00f3 d\u1ea5u tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u1edf t\u1eed s\u1ed1. Kho\u1ea3ng c\u00e1ch b\u1eb1ng 0 khi \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>L\u00e0m sao t\u00ecm h\u00ecnh chi\u1ebfu c\u1ee7a \u0111i\u1ec3m l\u00ean \u0111\u01b0\u1eddng th\u1eb3ng?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua M v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi \u0394 (nh\u1eadn vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0394 l\u00e0m vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng), r\u1ed3i gi\u1ea3i h\u1ec7 \u0111\u1ec3 t\u00ecm giao \u0111i\u1ec3m H c\u1ee7a hai \u0111\u01b0\u1eddng. \u0110\u1ed9 d\u00e0i MH ch\u00ednh l\u00e0 kho\u1ea3ng c\u00e1ch.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau b\u1eb1ng bao nhi\u00eau?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau c\u00f3 kho\u1ea3ng c\u00e1ch b\u1eb1ng 0 v\u00ec ch\u00fang c\u00f3 \u0111i\u1ec3m chung. C\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch ch\u1ec9 \u00e1p d\u1ee5ng cho hai \u0111\u01b0\u1eddng th\u1eb3ng song song (trong m\u1eb7t ph\u1eb3ng) ho\u1eb7c ch\u00e9o nhau (trong kh\u00f4ng gian).<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng b\u1eb1ng m\u00e1y t\u00ednh Casio \u0111\u01b0\u1ee3c kh\u00f4ng?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1ee3c. B\u1ea1n nh\u1eadp bi\u1ec3u th\u1ee9c |aX + bY + c| \u00f7 \u221a(a\u00b2 + b\u00b2), d\u00f9ng ph\u00edm CALC \u0111\u1ec3 thay X = x\u2080, Y = y\u2080. Trong kh\u00f4ng gian, c\u00f3 th\u1ec3 d\u00f9ng ch\u1ebf \u0111\u1ed9 Vector c\u1ee7a m\u00e1y \u0111\u1ec3 t\u00ednh t\u00edch c\u00f3 h\u01b0\u1edbng.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>K\u1ebft lu\u1eadn<\/b><\/h2>\n<p style=\"text-align: justify;\"><b>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/b><span style=\"font-weight: 400;\"> l\u00e0 \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n vu\u00f4ng g\u00f3c t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng. Trong m\u1eb7t ph\u1eb3ng Oxy, b\u1ea1n ch\u1ec9 c\u1ea7n \u0111\u01b0a \u0111\u01b0\u1eddng th\u1eb3ng v\u1ec1 d\u1ea1ng t\u1ed5ng qu\u00e1t r\u1ed3i \u00e1p d\u1ee5ng d = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2); trong kh\u00f4ng gian Oxyz, d\u00f9ng t\u00edch c\u00f3 h\u01b0\u1edbng d = |[AM\u2192, u\u2192]| \/ |u\u2192|. H\u00e3y l\u01b0u l\u1ea1i b\u1ea3ng t\u1ed5ng h\u1ee3p \u0111\u1ec3 tra nhanh khi l\u00e0m b\u00e0i.<\/span><\/p>\n<p style=\"text-align: justify;\"><b>Xem th\u00eam:<\/b><\/p>\n<ul>\n<li>\n<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-huu-ti-la-gi\/\">S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng c\u1ee7a c\u00e1c s\u1ed1 trong To\u00e1n h\u1ecdc<\/a><\/p>\n<\/li>\n<li>\n<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/\">B\u1ed9 c\u00f4ng th\u1ee9c Ho\u00e1n v\u1ecb \u2013 Ch\u1ec9nh h\u1ee3p \u2013 T\u1ed5 h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t trong To\u00e1n h\u1ecdc<\/a><\/p>\n<\/li>\n<\/ul>\n<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"C\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch t\u1eeb 1 \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"V\u1edbi \u0111i\u1ec3m M(x\u2080; y\u2080) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng ax + by + c = 0, kho\u1ea3ng c\u00e1ch l\u00e0 d = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2).\"}},{\"@type\":\"Question\",\"name\":\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng h\u1ecdc \u1edf l\u1edbp m\u1ea5y?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"C\u00f4ng th\u1ee9c trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 10; c\u00f4ng th\u1ee9c trong kh\u00f4ng gian Oxyz \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 12.\"}},{\"@type\":\"Question\",\"name\":\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 \u00e2m kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Kh\u00f4ng. Kho\u1ea3ng c\u00e1ch lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0, v\u00ec v\u1eady c\u00f4ng th\u1ee9c c\u00f3 d\u1ea5u tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u1edf t\u1eed s\u1ed1. Kho\u1ea3ng c\u00e1ch b\u1eb1ng 0 khi \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng.\"}},{\"@type\":\"Question\",\"name\":\"L\u00e0m sao t\u00ecm h\u00ecnh chi\u1ebfu c\u1ee7a \u0111i\u1ec3m l\u00ean \u0111\u01b0\u1eddng th\u1eb3ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua M v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi \u0394 (nh\u1eadn vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0394 l\u00e0m vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng), r\u1ed3i gi\u1ea3i h\u1ec7 \u0111\u1ec3 t\u00ecm giao \u0111i\u1ec3m H c\u1ee7a hai \u0111\u01b0\u1eddng. \u0110\u1ed9 d\u00e0i MH ch\u00ednh l\u00e0 kho\u1ea3ng c\u00e1ch.\"}},{\"@type\":\"Question\",\"name\":\"Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau b\u1eb1ng bao nhi\u00eau?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau c\u00f3 kho\u1ea3ng c\u00e1ch b\u1eb1ng 0 v\u00ec ch\u00fang c\u00f3 \u0111i\u1ec3m chung. C\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch ch\u1ec9 \u00e1p d\u1ee5ng cho hai \u0111\u01b0\u1eddng th\u1eb3ng song song (trong m\u1eb7t ph\u1eb3ng) ho\u1eb7c ch\u00e9o nhau (trong kh\u00f4ng gian).\"}},{\"@type\":\"Question\",\"name\":\"T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng b\u1eb1ng m\u00e1y t\u00ednh Casio \u0111\u01b0\u1ee3c kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u01b0\u1ee3c. B\u1ea1n nh\u1eadp bi\u1ec3u th\u1ee9c |aX + bY + c| \u00f7 \u221a(a\u00b2 + b\u00b2), d\u00f9ng ph\u00edm CALC \u0111\u1ec3 thay X = x\u2080, Y = y\u2080. Trong kh\u00f4ng gian, c\u00f3 th\u1ec3 d\u00f9ng ch\u1ebf \u0111\u1ed9 Vector c\u1ee7a m\u00e1y \u0111\u1ec3 t\u00ednh t\u00edch c\u00f3 h\u01b0\u1edbng.\"}}]}<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb \u0111i\u1ec3m \u0111\u00f3 \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng. Trong m\u1eb7t ph\u1eb3ng Oxy, v\u1edbi \u0111i\u1ec3m M(x\u2080; y\u2080) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0394: ax + by + c = 0, c\u00f4ng th\u1ee9c l\u00e0 d(M, \u0394) = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2). C\u00f4ng [&hellip;]<\/p>\n","protected":false},"author":84,"featured_media":622354,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng","_yoast_wpseo_title":"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: C\u00f4ng th\u1ee9c Oxy, Oxyz","_yoast_wpseo_metadesc":"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng t\u00ednh b\u1eb1ng d = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2). Xem c\u00f4ng th\u1ee9c Oxy, Oxyz, v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i v\u00e0 b\u1ea3ng t\u1ed5ng h\u1ee3p.","footnotes":""},"categories":[29235,3910,30453],"tags":[],"class_list":["post-620676","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-goc-to-mo","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: C\u00f4ng th\u1ee9c Oxy, Oxyz<\/title>\n<meta name=\"description\" content=\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng t\u00ednh b\u1eb1ng d = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2). Xem c\u00f4ng th\u1ee9c Oxy, Oxyz, v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i v\u00e0 b\u1ea3ng t\u1ed5ng h\u1ee3p.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/khoang-cach-tu-diem-den-duong-thang\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: C\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5\" \/>\n<meta property=\"og:description\" content=\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng t\u00ednh b\u1eb1ng d = |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2). Xem c\u00f4ng th\u1ee9c Oxy, Oxyz, v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i v\u00e0 b\u1ea3ng t\u1ed5ng h\u1ee3p.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/khoang-cach-tu-diem-den-duong-thang\/\" \/>\n<meta property=\"og:site_name\" content=\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:published_time\" content=\"2026-11-09T02:29:28+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-11-09T02:35:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/khoang-cach-tu-diem-den-duong-thang.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Daisy Daisy\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi\" \/>\n\t<meta name=\"twitter:data1\" content=\"Daisy Daisy\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 ph\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/\"},\"author\":{\"name\":\"Daisy Daisy\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/person\\\/fbfb09918671f672a65debf20f905308\"},\"headline\":\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: C\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5\",\"datePublished\":\"2026-11-09T02:29:28+00:00\",\"dateModified\":\"2026-11-09T02:35:59+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/\"},\"wordCount\":1893,\"publisher\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2026\\\/11\\\/khoang-cach-tu-diem-den-duong-thang.jpg\",\"articleSection\":[\"G\u00f3c t\u00f2 m\u00f2\",\"Kh\u00e1m Ph\u00e1\",\"Ki\u1ebfn Th\u1ee9c\"],\"inLanguage\":\"vi\",\"copyrightYear\":\"2026\",\"copyrightHolder\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/\",\"name\":\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: C\u00f4ng th\u1ee9c Oxy, Oxyz\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/khoang-cach-tu-diem-den-duong-thang\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2026\\\/11\\\/khoang-cach-tu-diem-den-duong-thang.jpg\",\"datePublished\":\"2026-11-09T02:29:28+00:00\",\"dateModified\":\"2026-11-09T02:35:59+00:00\",\"description\":\"Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng t\u00ednh b\u1eb1ng d = |ax\u2080 + by\u2080 + c| \\\/ \u221a(a\u00b2 + b\u00b2). 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