{"id":3663,"date":"2024-01-30T12:23:31","date_gmt":"2024-01-30T06:23:31","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3663"},"modified":"2024-10-29T17:19:37","modified_gmt":"2024-10-29T11:19:37","slug":"line-divisor-point","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/line-divisor-point\/","title":{"rendered":"\u09b0\u09c7\u0996\u09be \u09ac\u09bf\u09ad\u0995\u09cd\u09a4\u0995\u09be\u09b0\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995, \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5"},"content":{"rendered":"<h2><span style=\"color: #339966;\"><b>\u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5 <\/b><b>(<\/b><b>Locus)<\/b><\/span><\/h2>\n<p><img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/locus-of-points.png\" alt=\"\u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5\" width=\"355\" height=\"329\" \/><\/p>\n<p><span 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\u09b8\u09be\u09a5\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964<\/span><\/p>\n<ol>\n<li><b> <\/b><span style=\"font-weight: 400;\">\u09a6\u09c1\u0987\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 C, D \u09a5\u09c7\u0995\u09c7 \u09b8\u09ae\u09a6\u09c2\u09b0\u09ac\u09b0\u09cd\u09a4\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5 CD \u09b0\u09c7\u0996\u09be\u0982\u09b6\u09c7\u09b0 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995 <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.youtube.com\/watch?v=cB0DqOSL26M&amp;list=PL1pf33qWCkmidHi8s0NpGydwZAj3fGIhQ&amp;index=1\" target=\"_blank\" rel=\"noopener\">\u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be<\/a><\/span>\u0964 \u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">PC\u00a0=\u00a0PD\u00a0<\/span><span style=\"font-weight: 400;\">\u09b6\u09b0\u09cd\u09a4\u09be\u09a7\u09c0\u09a8\u09c7 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09b2\u09ae\u09be\u09a8, \u09af\u09c7\u0996\u09be\u09a8\u09c7 PC \u0993 PD \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 C \u0993 D \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u09c1\u099d\u09be\u09af\u09bc\u0964<\/span><\/li>\n<li><b> <\/b><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0995\u09cb\u09a3 <span class=\"katex-eq\" data-katex-display=\"false\">\\angle A B C<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09b0 \u09ac\u09be\u09b9\u09c1 \u09a6\u09c1\u0987\u099f\u09bf \u09b9\u09a4\u09c7 \u09af\u09c7 \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 P \u098f\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b8\u09ae\u09be\u09a8, \u09a4\u09be\u09b0 \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5 \u0989\u0995\u09cd\u09a4 \u0995\u09cb\u09a3\u09c7\u09b0 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u0995 \u09b0\u09c7\u0996\u09be\u0964<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">PM\u00a0=\u00a0PN\u00a0<\/span><span style=\"font-weight: 400;\">\u09b6\u09b0\u09cd\u09a4\u09be\u09a7\u09c0\u09a8\u09c7 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u099a\u09b2\u09ae\u09be\u09a8 \u09af\u09c7\u0996\u09be\u09a8\u09c7 PN \u0993 PM, P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 BA \u0993 BC \u09ac\u09be\u09b9\u09c1\u09b0 \u0989\u09aa\u09b0 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c1\u099d\u09be\u09af\u09bc\u0964<\/span><\/p>\n<p><b>iii. <\/b><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 O \u09a5\u09c7\u0995\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5 \u098f\u0995\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4, \u09af\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0990 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0993 \u09af\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u0990 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac a. \u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">OP\u00a0=\u00a0a\u00a0<\/span><span style=\"font-weight: 400;\">\u09b6\u09b0\u09cd\u09a4\u09be\u09a7\u09c0\u09a8\u09c7 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 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\u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09a4\u09c7 \u099a\u09bf\u09a4\u09cd\u09b0 \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>ii.<\/strong> \u09b8\u09c7\u099f\u09ad\u09c1\u0995\u09cd\u09a4 \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 (x, y) \u09a7\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><b>iii. <\/b><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b6\u09b0\u09cd\u09a4 \u09ae\u09a4\u09c7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf\u09b0 \u09ad\u09c2\u099c x \u098f\u09ac\u0982 \u0995\u09cb\u099f\u09bf y \u098f\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>iv<\/strong>. (iii) \u09a8\u0982 \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u0995\u09c7 \u09b8\u09b0\u09b2 \u0995\u09b0\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09ac\u09c7 \u0964<\/span><\/p>\n<h2><span style=\"color: #339966;\"><b>\u09b0\u09c7\u0996\u09be \u09ac\u09bf\u09ad\u0995\u09cd\u09a4\u0995\u09be\u09b0\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 <\/b><b>(Coordinates of a line divisor point)<\/b><\/span><\/h2>\n<h3><span style=\"color: #800080;\"><b>\u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ac\u09bf\u09ad\u09be\u0997\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{P}\\left(\\mathrm{x}_{1}, \\mathrm{y}_{1}\\right)<\/span> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{Q}\\left(\\mathrm{x}_{2}, \\mathrm{y}_{2}\\right)<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u0982\u09af\u09cb\u0997 \u09b0\u09c7\u0996\u09be\u0982\u09b6 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{R}(\\mathrm{x}, \\mathrm{y})<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}_{1}: \\mathrm{m}_{2}<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u09b9\u09af\u09bc\u09c7\u099b\u09c7\u0964 R \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/academic\/10\/\">\u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995<\/a><\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u098f\u0996\u09be\u09a8\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">PR : RQ = m_{1} : m_{2}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P, Q, R<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a5\u09c7\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">O X<\/span> \u098f\u09b0 \u0989\u09aa\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">P A, Q B, R C<\/span> \u09b2\u09ae\u09cd\u09ac \u0986\u0981\u0995\u09bf\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">PS \\perp RC<\/span><\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">RT \\perp QB<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">\\triangle \\mathrm{PRS}<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">\\triangle \\mathrm{ORT}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b8\u09a6\u09c3\u09b6 \u09ac\u09b2\u09c7<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P S}{R T}=\\frac{R S}{Q T}=\\frac{P R}{R Q}=\\frac{m_{1}}{m_{2}} \\ldots \\ldots . . .(1)<\/span>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0, <span class=\"katex-eq\" data-katex-display=\"false\">P S=A C=O C-O A=x-x_{1}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u09ac\u0982, <span class=\"katex-eq\" data-katex-display=\"false\">R T=C B=O B-O C=x_{2}-x<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore<\/span><\/span> <span style=\"font-weight: 400;\">(1) \u09a5\u09c7\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P S}{R T}=\\frac{m_{1}}{m_{2}}<\/span> <\/span><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\mathrm{x}-\\mathrm{x}_{1}}{\\mathrm{x}_{2}-\\mathrm{x}}=\\frac{m_{1}}{m_{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">m_{2} x-m_{2} x_{1}=m_{1} x_{2}-m_{1} x<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\left(m_{1}+m_{2}\\right) x=m_{1} x_{2}+m_{2} x_{1}<\/span><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore x=\\frac{\\mathrm{m}_{1} \\mathrm{x}_{2}+\\mathrm{m}_{2} \\mathrm{x}_{1}}{\\mathrm{~m}_{1}+\\mathrm{m}_{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">R S=R C-C S=y-y_{1}<\/span> <\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982\u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">Q T=B Q-B T=y_{2}-y<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a6\u09cd\u09b0\u09c1\u09aa,<\/span> <span style=\"font-weight: 400;\">(1) \u09a5\u09c7\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{R S}{Q T}=\\frac{m_{1}}{m_{2}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09be, <\/span><span style=\"font-weight: 400;\">\u00a0<span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\mathrm{y}-\\mathrm{y}_{1}}{\\mathrm{y}_{2}-\\mathrm{y}}=\\frac{m_{1}}{m_{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">m_{2} y-m_{2} y_{1}=m_{1} y_{2}-m_{1} y<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\left(m_{1}+m_{2}\\right) y=m_{1} y_{2}+m_{2} y_{1}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore x=\\frac{\\mathrm{m}_{1} \\mathrm{y}_{2}+\\mathrm{m}_{2} \\mathrm{y}_{1}}{\\mathrm{~m}_{1}+\\mathrm{m}_{2}}<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4\u0995\u09be\u09b0\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 <span class=\"katex-eq\" data-katex-display=\"false\">=\\left(\\frac{m_{1} x_{2}+m_{2} x_{1}}{m_{1}+m_{2}}, \\frac{m_{1} y_{2}+m_{2} y_{1}}{m_{1}+m_{2}}\\right)<\/span><\/span><\/p>\n<p><b>\u0985\u09a8\u09c1\u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4 1<\/b><b>: <\/b><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{R}, \\mathrm{PQ}<\/span> \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">m_{1}=m_{2}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\mathrm{P}\\left(\\mathrm{x}_{1}, \\mathrm{y}_{1}\\right)<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{Q}\\left(\\mathrm{x}_{2}, \\mathrm{y}_{2}\\right)<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u0982\u09af\u09cb\u0997 \u09b0\u09c7\u0996\u09be\u0982\u09b6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995,\u00a0<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\frac{x_{1}+x_{2}}{2}, \\frac{y_{1}+y_{2}}{2}\\right)<\/span>\n<p><b>\u0985\u09a8\u09c1\u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4 2<\/b> <b>: <\/b><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf R \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf PQ \u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{k}: 1<\/span> \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\">PR: RQ = <span class=\"katex-eq\" data-katex-display=\"false\">k: 1<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09af\u09bc \u09a4\u09be\u09b9\u09b2\u09c7,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x=\\frac{k x_{2}+x_{1}}{k+1}<\/span>\u00a0 \u098f\u09ac\u0982,\u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{y}=\\frac{k y_{2}+y_{1}}{k+1}<\/span><\/span><span style=\"font-weight: 400;\"> , \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b6\u09c1\u09a7\u09c1 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{k}<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u099c\u09be\u09a8\u09b2\u09c7 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u099c\u09be\u09a8\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n<p><b>(b) \u09ac\u09b9\u09bf\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4\u09bf\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/b><\/p>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf , <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{R}<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{PQ}<\/span> \u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">mathrm{m}_{1}: \\mathrm{m}_{2}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u00a0\u098f \u09ac\u09b9\u09bf\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09c7\u099b\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{PR}: \\mathrm{RQ}=\\mathrm{m}_{1}: \\mathrm{m}_{2}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P R}{Q R}=\\frac{m_{1}}{m_{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\triangle<\/span><\/span><span style=\"font-weight: 400;\">PRS \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\triangle<\/span><\/span><span style=\"font-weight: 400;\">QRT \u09b8\u09a6\u09c3\u09b6\u0964<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P S}{Q T}=\\frac{R S}{R T}=\\frac{P R}{Q R}=\\frac{m_{1}}{m_{2}} \\ldots \\ldots . . .(1)<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore<\/span><\/span> <span style=\"font-weight: 400;\">(1) \u09a5\u09c7\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P S}{Q T}=\\frac{m_{1}}{m_{2}}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\mathrm{x}-\\mathrm{x}_{1}}{\\mathrm{x}-\\mathrm{x}_{2}}=\\frac{m_{1}}{m_{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">m_{1} x-m_{1} x_{2}=m_{2} x-m_{2} x_{1}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\left(m_{1}-m_{2}\\right) x=m_{1} x_{2}-m_{2} x_{1}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore x=\\frac{\\mathrm{m}_{1} \\mathrm{x}_{2}-\\mathrm{m}_{2} \\mathrm{x}_{1}}{\\mathrm{~m}_{1}-\\mathrm{m}_{2}}<\/span>\n<p><span style=\"font-weight: 400;\">\u09a4\u09a6\u09cd\u09b0\u09c1\u09aa,<\/span> <span style=\"font-weight: 400;\">(1) \u09a5\u09c7\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{R S}{R T}=\\frac{m_{1}}{m_{2}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09be, <\/span><span style=\"font-weight: 400;\">\u00a0<span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\mathrm{y}-\\mathrm{y}_{1}}{\\mathrm{y}-\\mathrm{y}_{2}}=\\frac{m_{1}}{m_{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">m_{1} y-m_{1} y_{2}=m_{2} y-m_{2} y_{1}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\left(m_{1}-m_{2}\\right) y=m_{1} y_{2}-m_{2} y_{1}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore y=\\frac{\\mathrm{m}_{1} \\mathrm{y}_{2}-\\mathrm{m}_{2} \\mathrm{y}_{1}}{\\mathrm{~m}_{1}-\\mathrm{m}_{2}}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\text { \u09ac\u09b9\u09bf\u09ac\u09bf\u09ad\u0995\u09cd\u09a4\u0995\u09be\u09b0\u09c0 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 }\\left(\\frac{m_{1} x_{2}-m_{2} x_{1}}{m_{1}-m_{2}}, \\frac{m_{1} y_{2}-m_{2} y_{1}}{m_{1}-m_{2}}\\right)<\/span>\n<p>&nbsp;<\/p>\n<div class=\"x1tlxs6b x1g8br2z x1gn5b1j x230xth x14ctfv x1okitfd x6ikm8r x10wlt62 x1mzt3pk x1y1aw1k xn6708d xwib8y2 x1ye3gou x1n2onr6 x13faqbe x1vjfegm\" role=\"none\">\n<div class=\"\">\n<div class=\"x9f619 x1n2onr6 x1ja2u2z __fb-light-mode\" role=\"none\">\n<hr \/>\n<p dir=\"auto\" role=\"none\">\n<p class=\"x6prxxf x1fc57z9 x1yc453h x126k92a xzsf02u\" dir=\"auto\" role=\"none\"><em><strong>\u098f\u0987\u099a\u098f\u09b8\u09b8\u09bf \u0993 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be\u09b0\u09cd\u09a5\u09c0\u09a6\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\n<\/div>\n<\/div>\n<\/div>\n<ul>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-25-online-batch-2-bangla-english-ict\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a \u09e8.\u09e6 (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-26-online-batch-bangla-english-ict\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2025-online-batch\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2026-online-batch\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/medical-admission-course\/\">\u09ae\u09c7\u09a1\u09bf\u0995\u09c7\u09b2 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-a-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-b-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/buet-ques-solve\/\">\u09ac\u09c1\u09df\u09c7\u099f \u0995\u09cb\u09b6\u09cd\u099a\u09c7\u09a8 \u09b8\u09b2\u09ad \u0995\u09cb\u09b0\u09cd\u09b8<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-a-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-b-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<\/ul>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><em><strong>\u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u0995\u09bf\u09b2 \u09a1\u09c7\u09ad\u09c7\u09b2\u09aa\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/study-abroad-complete-guideline\/\">\u09ac\u09bf\u09a6\u09c7\u09b6\u09c7 \u0989\u099a\u09cd\u099a\u09b6\u09bf\u0995\u09cd\u09b7\u09be: Study Abroad Complete Guideline<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/student-hacks\/\">Student Hacks<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ielts-course\/\">IELTS Course by Munzereen Shahid<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/english-grammar-course\/\">Complete English Grammar Course<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ms-bundle\/\"> Microsoft Office 3 in 1 Bundle<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ghore-boshe-freelancing\/\">\u0998\u09b0\u09c7 \u09ac\u09b8\u09c7 Freelancing<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/facebook-marketing\/\">Facebook Marketing<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/adobe-4-in-1-bundle\/\">Adobe 4 in 1 Bundle<\/a><\/span><\/li>\n<\/ul>\n<hr \/>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em>\u09e7<\/em><em>\u09e6 \u09ae\u09bf\u09a8\u09bf\u099f \u09b8\u09cd\u0995\u09c1\u09b2\u09c7\u09b0 \u0995\u09cd\u09b2\u09be\u09b8\u0997\u09c1\u09b2\u09cb \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09a4\u09c7 \u09ad\u09bf\u099c\u09bf\u099f: <span style=\"color: #993300;\"><strong><a style=\"color: #993300;\" href=\"https:\/\/10minuteschool.com\/?ref=https%3A%2F%2Fblog.10minuteschool.com%2Fwordpress%2F&amp;post_id=78178&amp;blog_category_id=700\">www.10minuteschool.com<\/a><\/strong><\/span><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5 (Locus) \u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09a4\u09b2\u09c7 \u098f\u0995 \u09ac\u09be \u098f\u0995\u09be\u09a7\u09bf\u0995 \u09b6\u09b0\u09cd\u09a4\u09be\u09a7\u09c0\u09a8\u09c7 \u099a\u09b2\u09ae\u09be\u09a8 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09af\u09c7 \u09b8\u09b0\u09b2 \u09ac\u09be \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be\u09af\u09bc \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a4\u09be\u0995\u09c7 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b6\u09b0\u09cd\u09a4\u09be\u09a7\u09c0\u09a8\u09c7 \u0990 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09bf\u0995 \u099c\u09cd\u09af\u09be\u09ae\u09bf\u09a4\u09bf \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u09a8\u09bf\u099a\u09c7\u09b0 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u099e\u09cd\u099a\u09be\u09b0\u09aa\u09a5\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09aa\u09b0\u09bf\u099a\u09bf\u09a4\u0964 \u09a6\u09c1\u0987\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 C, D \u09a5\u09c7\u0995\u09c7<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/line-divisor-point\/\">Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4258,3037,3026],"tags":[2537,2538,2539,2536,2535],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3663"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3663"}],"version-history":[{"count":10,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3663\/revisions"}],"predecessor-version":[{"id":16102,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3663\/revisions\/16102"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}