{"id":11031,"date":"2021-05-27T15:45:37","date_gmt":"2021-05-27T10:15:37","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=11031"},"modified":"2021-10-12T22:04:58","modified_gmt":"2021-10-12T16:34:58","slug":"03-02-02","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/03-02-02\/","title":{"rendered":"03.02.02-\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc0\u0dd2\u0dc1\u0dda\u0dc2 \u0d86\u0d9a\u0dcf\u0dbb"},"content":{"rendered":"\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1V7RWunm1xD6vLeD8lCn1S2Xo2hhlaiEz&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0d85\u0db7\u0dd2\u0dbd\u0db8\u0dca\u0db7 \u0d86\u0d9a\u0dcf\u0dbb\u0dba<\/strong>(<span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm{xcos\u03b1}\\;+\\;\\mathrm{ysin\u03b2}\\;=\\;\\mathrm P<\/span>)<\/h3>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0db8\u0dd9\u0dc4\u0dd2 p \u0dba\u0db1\u0dd4 \u0db8\u0dd6\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u0dc3\u0dbb\u0dbd\u00a0\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dd2 \u0dbd\u0db8\u0dca\u0db6\u0d9a \u0daf\u0dd4\u0dbb \u0dc0\u0db1 \u0d85\u0dad\u0dbb<span class=\"wp-katex-eq\" data-display=\"false\">\\alpha<\/span> \u0dba\u0db1\u0dd4 \u0d91\u0db8 \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dba\u00a0x- \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0db0\u0db1 \u0daf\u0dd2\u0dc1\u0dcf\u0dc0 \u0dc3\u0db8\u0d9c \u0dc3\u0dcf\u0daf\u0db1 \u0d9a\u0ddd\u0dab\u0dba \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"532\" height=\"428\" class=\"wp-image-11972\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-189.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-189.png 532w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-189-300x241.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-189-150x121.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-189-522x420.png 522w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba (x,y) \u0dc3\u0dbd\u0d9a\u0db8\u0dd4 .<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}OA&amp;=&amp;P\\\\OT+TA&amp;=&amp;P\\\\OT+NP&amp;=&amp;P\\\\OM\\cos\\;\\alpha\\;+\\;MP\\sin\\;\\alpha&amp;=&amp;P\\\\x\\;\\cos\\;\\alpha\\;+\\;y\\;\\sin\\;\\alpha&amp;=&amp;P\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf: \u00a03x+4y+15=0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0db8\u0dd6\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u0d87\u0dad\u0dca \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0daf\u0dd4\u0dbb\u0daf \u0db8\u0dd9\u0db8 \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dba x &#8211; \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0db0\u0db1 \u0daf\u0dd2\u0dc1\u0dcf\u0dc0 \u0dc3\u0db8\u0d9c \u0dc3\u0dcf\u0daf\u0db1 \u0d9a\u0ddd\u0dab\u0dba\u0daf \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}3x+4y+15&amp;=&amp;0\\\\-3x-4y&amp;=&amp;15\\\\-\\frac35x-\\frac45y&amp;=&amp;3\\\\-x\\cos\\left(\\alpha\\right)-y\\sin\\left(\\alpha\\right)&amp;=&amp;3\\\\x\\cos\\left(\\pi-\\alpha\\right)+y\\sin\\left(\\pi-\\alpha\\right)&amp;=&amp;3\\end{array}<\/span>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"113\" height=\"164\" class=\"wp-image-11982\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-190.png\" alt=\"\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-group\">\r\n<div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\r\n<p class=\"has-text-align-center\">\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\cos\\;\\alpha\\;=\\;\\frac35<\/span> <span class=\"wp-katex-eq\" data-display=\"false\">\\sin\\;\\alpha\\;=\\;\\frac45<\/span><\/p>\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore<\/span>\u0db8\u0dd6\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dca \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0daf\u0dd4\u0dbb \u0d92\u0d9a\u0d9a 3\u0d9a\u0dca \u0dc0\u0dda. \u0db8\u0dd9\u0db8 \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dba \u00a0x &#8211; \u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0db0\u0db1 \u0daf\u0dd2\u0dc1\u0dcf\u0dc0 \u0dc3\u0db8\u0d9c \u0dc3\u0dcf\u0daf\u0db1 \u0d9a\u0ddd\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\pi+\\alpha<\/span> \u00a0\u0dc0\u0dda. \u0db8\u0dd9\u0dc4\u0dd2 <span class=\"wp-katex-eq\" data-display=\"false\">\\alpha=\\;\\sin^{-1}\\left(\\frac45\\right)<\/span> \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0db8\u0dd9\u0db8 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0db4\u0dca\u200d\u0dbb\u0dc3\u0dca\u0dae\u0dcf\u0dbb\u0dba \u0db4\u0dc4\u0dad \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"372\" height=\"319\" class=\"wp-image-11988\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-191.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-191.png 372w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-191-300x257.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-191-150x129.png 150w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0d86\u0d9a\u0dcf\u0dbb\u0dba<\/strong><\/h3>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>A = (<span class=\"wp-katex-eq\" data-display=\"false\">x_0<\/span>,<span class=\"wp-katex-eq\" data-display=\"false\">y_0<\/span>)\u00a0\u0dba\u0db1\u0dd4 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0daf\u0dd9\u0db1 \u0dbd\u0daf \u0d85\u0da0\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0d9a\u0dca \u0dba\u0dd0\u0dba\u0dd2\u0daf \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a x &#8211;\u00a0\u0d85\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0db0\u0db1 \u0daf\u0dd2\u0dc1\u0dcf\u0dc0 \u0dc3\u0db8\u0d9c \u0dc3\u0dcf\u0daf\u0db1 \u0d9a\u0ddd\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\alpha<\/span> \u00a0\u0dbd\u0dd9\u0dc3\u0daf \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"429\" height=\"355\" class=\"wp-image-11990\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-192.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-192.png 429w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-192-300x248.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/02\/image-192-150x124.png 150w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba (x,y) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0dc3\u0dbd\u0d9a\u0db8\u0dd4<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda\u00a0 \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba (m)<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac{y-y_0}{x-x_0}=\\tan\\;\\alpha<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{y-y_0}{x-x_0}=\\frac{\\sin\\;\\mathrm\\alpha}{\\cos\\;\\mathrm\\alpha}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{y-y_0}{\\sin\\;\\alpha}=\\frac{\\mathrm x-{\\mathrm x}_0}{\\cos\\;\\mathrm\\alpha}(=t\\;\\text{\u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4})<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\mathrm x-{\\mathrm x}_0}{\\cos\\;\\mathrm\\alpha}=\\;t\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\mathrm x=\\;\\mathrm t\\;\\mathrm{cos\u03b1}+{\\mathrm x}_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{y-y_0}{\\sin\\;\\mathrm\\alpha}=\\;t\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\mathrm y=\\;\\mathrm t\\;\\sin\\alpha+{\\mathrm y}_0<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d91\u0db8 \u0db1\u0dd2\u0dc3\u0dcf \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a <span class=\"wp-katex-eq\" data-display=\"false\">=(\\mathrm{tcos}\\;\\mathrm\\alpha+{\\mathrm x}_0\\;,\\;\\mathrm{tsin}\\;\\mathrm\\alpha+{\\mathrm y}_0)<\/span>\u00a0 \u00a0\u00a0\u00a0\u00a0<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0db8\u0dd9\u0dc4\u0dd2 t\u00a0\u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"has-inline-color has-vivid-red-color\">\u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0d89\u0dc0\u0dad\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dbd\u0dd0\u0db6\u0dda.<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf: \u00a0x &#8211; y + 1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad (1, 2) \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u0d91\u0db8 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0d92\u0d9a\u0d9a <span class=\"wp-katex-eq\" data-display=\"false\">3\\sqrt2<\/span>\u00a0\u0daf\u0dd4\u0dbb\u0dd2\u0db1\u0dca \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd2 \u0dbd\u0d9a\u0dca\u0dc2\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"242\" height=\"182\" class=\"wp-image-12001\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image.png 242w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-150x113.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-80x60.png 80w\" sizes=\"(max-width: 242px) 100vw, 242px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0d95\u0db1\u0dd1\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0d9a\u0dca P(t , t+1)\u00a0\u0dbd\u0dd9\u0dc3 \u0d9c\u0dad \u0dc4\u0dd0\u0d9a.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sqrt{(t+1)^2\\;+\\;(t+1-2)^2}\\;=\\;AP<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sqrt{(\\mathrm t-1)^2\\;+\\;(\\mathrm t+1-2)^2}\\;=\\;3\\sqrt2<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2(\\mathrm t-1)^2\\;=\\;18<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">(\\mathrm t-1)^2\\;=\\;9<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm t\\;^2\\;-2t\\;+1\\;=\\;9<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm t\\;^2\\;-2t\\;+\\;8\\;=\\;0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\left(\\mathrm t-4\\right)\\left(\\mathrm t+2\\right)\\;=\\;0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\Rightarrow\\;\\;\\mathrm t=4\\;\\;,\\;\\;\\;\\;\\;\\;\\;\\mathrm t=-2<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2 \u0dc0\u0dbd \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a (4, 5) \u0dc4\u0dcf (-2, -1) \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<h4 class=\"wp-block-heading\"><strong><span class=\"has-inline-color\" style=\"color: #304170\">\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0dc4\u0dcf \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0d9a \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc0\u0dd2\u0da7 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dbd\u0db6\u0dcf \u0d9c\u0dd0\u0db1\u0dd3\u0db8(\u0d92\u0d9a \u0dbd\u0d9a\u0dca\u0dc2 \u0d86\u0d9a\u0dcf\u0dbb\u0dba)<\/span><\/strong><\/h4>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba m\u00a0\u0dba\u0dba\u0dd2\u0daf \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0daf\u0dd3 \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0d9a \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a <span class=\"wp-katex-eq\" data-display=\"false\">({\\mathrm x}_{0\\;\\;,\\;}{\\mathrm y}_0)<\/span>\u00a0 \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"403\" height=\"334\" class=\"wp-image-12006\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-1.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-1.png 403w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-1-300x249.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-1-150x124.png 150w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda\u00a0 \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">m\\;=\\;tan\\;\\theta<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u00a0\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">(x\u00a0,y)<\/span>\u00a0\u0dc3\u0dbd\u0d9a\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda\u00a0 \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba<span class=\"wp-katex-eq\" data-display=\"false\">=\\tan\\;\\theta\\;=\\;\\frac{y-y_0}{x-x_0}<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">m(x-x_0)\\;=y-y_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">y-y_0\\;=\\;m(x-x_0)<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf: \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\frac32<\/span>\u00a0\u0dc0\u0db1 (2, -3) \u0dbd\u0d9a\u0dca\u0dc2\u0dba \u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm y\\;-\\;(-3)\\;=\\;\\frac32\\left(\\mathrm x\\;-\\;2\\right)<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">3\\mathrm x\\;-\\;2\\mathrm y\\;-12\\;=\\;0<\/span><\/p>\r\n\r\n\r\n\r\n<h4 class=\"wp-block-heading\"><strong><span class=\"has-inline-color\" style=\"color: #304170\">\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a\u0dca \u0db8\u0dad \u0dbd\u0d9a\u0dca\u0dc2 \u0daf\u0dd9\u0d9a\u0d9a \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc0\u0dd2\u0da7 \u0d91\u0db8 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc3\u0dd9\u0dc0\u0dd3\u0db8.(\u0daf\u0dca\u0dc0\u0dd3 \u0dbd\u0d9a\u0dca\u0dc2 \u0d86\u0d9a\u0dcf\u0dbb\u0dba)<\/span><\/strong><\/h4>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a\u0dca \u0db8\u0dad \u0daf\u0dd9\u0db1 \u0dbd\u0daf \u0dbd\u0d9a\u0dca\u0dc2 \u0daf\u0dd9\u0d9a <span class=\"wp-katex-eq\" data-display=\"false\">A(x_{1\\;}\\;,\\;y_1)<\/span> \u0dc4\u0dcf <span class=\"wp-katex-eq\" data-display=\"false\">B(x_{2\\;}\\;,\\;y_2)<\/span> \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"303\" class=\"wp-image-12008\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-2.png\" alt=\"\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-2.png 366w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-2-300x248.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-2-150x124.png 150w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba (x , y) \u0dc3\u0dbd\u0d9a\u0db8\u0dd4<\/li>\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda\u00a0 \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba<span class=\"wp-katex-eq\" data-display=\"false\">=\\frac{y_2\\;-\\;y_1}{x_{2\\;}\\;-\\;x_1}<\/span><\/li>\r\n<li>\u0dad\u0dc0\u0daf \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda\u00a0\u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">=\\frac{y\\;-\\;y_1}{x\\;-\\;x_1}<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore\\;\\;\\;\\;\\;\\;\\frac{y\\;-\\;y_1}{x\\;-\\;x_1}\\;=\\;\\frac{y_2\\;-y_1}{x_{2\\;\\;}\\;-\\;x_1}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\Rightarrow\\;\\;\\;\\;y\\;-y_1\\;=\\frac{\\left(y_2\\;-\\;y_1\\right)}{\\left(x_2\\;-\\;x_1\\right)}\\left(x\\;-x_1\\right)<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf:\u00a0 (-1, 3), (5, 4)\u00a0 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0db1\u0dca \u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm y\\;-\\;3\\;=\\;\\frac{\\left(4\\;-\\;3\\right)}{\\left[5\\;-\\left(-1\\right)\\right]}\\left[\\mathrm x\\;\\;-\\left(-1\\right)\\right]<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm x\\;-\\;\\mathrm y\\;+\\;19\\;=\\;0<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1V7RWunm1xD6vLeD8lCn1S2Xo2hhlaiEz&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/drive\/folders\/1otlWj3tqtLlKXwTQeg1Fpf3aZMecmgUd?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc0\u0dd2\u0dc1\u0dda\u0dc2 \u0d86\u0d9a\u0dcf\u0dbb\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0db4\u0dad\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8 \u0dc3\u0dd2\u0daf\u0dd4 \u0d9a\u0dbb\u0dba\u0dd2.<\/p>\n","protected":false},"author":61,"featured_media":16874,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3665,3634,42,3630,3629],"tags":[3886,3887,3879,3880,3799,3873,3798,3811,3812,3882,3877,3881,3885,3884,3883,3876,3875,3878,3874],"class_list":{"0":"post-11031","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-03-02-straight-line","8":"category-03-coordinate-geometry","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-coordinates","13":"tag-cordinates","14":"tag-parameter","15":"tag-perpendicular","16":"tag-sarala-rekawa","17":"tag-sarala-rekhawa","18":"tag-straight-line","19":"tag-x-","20":"tag-y-","21":"tag-3882","22":"tag-3877","23":"tag-3881","24":"tag-3885","25":"tag-3884","26":"tag-3883","27":"tag-3876","28":"tag-3875","29":"tag-3878","30":"tag-3874"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/11031"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/61"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=11031"}],"version-history":[{"count":45,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/11031\/revisions"}],"predecessor-version":[{"id":32540,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/11031\/revisions\/32540"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media\/16874"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=11031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=11031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=11031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}