{"id":12682,"date":"2021-03-24T05:04:39","date_gmt":"2021-03-23T23:34:39","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=12682"},"modified":"2021-11-25T18:00:59","modified_gmt":"2021-11-25T12:30:59","slug":"03-02-05","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/03-02-05\/","title":{"rendered":"03.02.05 &#8211; \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0daf\u0dd9\u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0dc4\u0ddd \u0d91\u0d9a\u0db8 \u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd3\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dad\u0dcf\u0dc0"},"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<ul class=\"wp-block-list\">\r\n<li>A (x<sub>1<\/sub>, y<sub>1<\/sub>) \u0dc4\u0dcf B (x<sub>2<\/sub>, y<sub>2<\/sub>) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a lx + my + n = 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0d85\u0db1\u0dd4\u0db6\u0daf\u0dca\u0db0\u0dba\u0dd9\u0db1\u0dca \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0db1 \u0d86\u0d9a\u0dcf\u0dbb\u0dba \u0dc3\u0dbd\u0d9a\u0dcf \u0db6\u0dbd\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-34967 \" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/Pasted-into-03.02.05-\u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba-\u0daf\u0dd9\u0d9a\u0d9a\u0dca-\u0dc3\u0dbb\u0dbd-\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a-\u0daf\u0dd9\u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda-\u0dc4\u0ddd-\u0d91\u0d9a\u0db8-\u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda-\u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd3\u0db8-\u0dc3\u0db3\u0dc4\u0dcf-\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dad\u0dcf\u0dc0.png\" width=\"661\" height=\"661\" \/><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">AC\u2236CB=\\lambda\u22361<\/span> \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/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\">C\\equiv(\\frac{x_1+\\lambda x_2}{1+\\lambda}),(\\frac{y_1+\\lambda y_2}{1+\\lambda})<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0db8\u0dd9\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0dc0\u0dbd\u0dd2\u0db1\u0dca\u00a0 lx +my +n = 0 \u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0dda.<\/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\">\\begin{array}{rcl}l\\left(\\frac{x_1+\\lambda x_2}{1+\\lambda}\\right)+m\\left(\\frac{y_1+\\lambda y_2}{1+\\lambda}\\right)+n&amp;=&amp;0\\\\l(x_1+\u03bbx_2 )+m(y_1+\u03bby_2 )+n(\u03bb+1)&amp;=&amp;0\\\\(lx_2+my_2+n)\\lambda+lx_1+my_1+n&amp;=&amp;0\\\\\\lambda&amp;=&amp;-\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>A (x<sub>1<\/sub>, y<sub>1<\/sub>) \u0dc4\u0dcf B (x<sub>2<\/sub>, y<sub>2<\/sub>) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a lx + my + n = 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0daf\u0dd9\u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dba\u0dd2 \u0db1\u0db8\u0dca c \u0db8\u0d9c\u0dd2\u0db1\u0dca AB \u0d85\u0db7\u0dca\u200d\u0dba\u0db1\u0dca\u0dad\u0dbb\u0dc0 \u0db6\u0dd9\u0daf\u0dba\u0dd2<\/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\">\\begin{array}{rcl}\\lambda&amp;&gt;&amp;0\\\\&amp;&amp;\\\\-\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}&amp;&gt;&amp;0\\\\\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}&amp;&lt;&amp;0\\\\&amp;&amp;\\\\\\left(\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}\\right)\\times(lx_2+my_2+n)^2&amp;&lt;&amp;0\\\\&amp;&amp;\\\\(lx_1+my_1+n)(lx_2+my_2+n)&amp;&lt;&amp;0\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>A (x<sub>1<\/sub>, y<sub>1<\/sub>) \u0dc4\u0dcf B (x<sub>2<\/sub>, y<sub>2<\/sub>) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0daf\u0dd9\u0d9a lx + my + n = 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0d91\u0d9a\u0db8 \u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dba\u0dd2 \u0db1\u0db8\u0dca c \u0db8\u0d9c\u0dd2\u0db1\u0dca AB \u0db6\u0dcf\u0dc4\u0dd2\u0dbb\u0dc0 \u0db6\u0dd9\u0daf\u0dba\u0dd2.<\/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\">\\begin{array}{rcl}\\lambda&amp;&lt;&amp;0\\\\&amp;&amp;\\\\-\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}&amp;&lt;&amp;0\\\\&amp;&amp;\\\\\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}&amp;&gt;&amp;0\\\\&amp;&amp;\\\\\\left(\\frac{(lx_1+my_1+n)}{(lx_2+my_2+n)}\\right)(lx_2+my_2+n)^2&amp;&gt;&amp;0\\\\&amp;&amp;\\\\(lx_1+my_1+n)(lx_2+my_2+n)&amp;&gt;&amp;0\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf1: 2x-3y+1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0dc3\u0dcf\u0db4\u0dda\u0d9a\u0dca\u0dc2\u0dc0 (2,3 )\u0dc4\u0dcf (-5,7) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0d91\u0d9a\u0db8 \u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0daf \u0daf\u0dd9\u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda\u0daf \u0dba\u0db1\u0dca\u0db1\u00a0\u0dc3\u0ddc\u0dba\u0dcf \u0db6\u0dbd\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">E=(2\\times2-3\\times3+1)\\lbrack2\\times(-5)-3\\times7+1\\rbrack<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\;\\;\\;=120&gt;0\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d91\u0d9a\u0db8 \u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dba\u0dd2.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center has-background\" style=\"background-color: #272062\"><span style=\"color: #ffffff\"><em><strong><span style=\"font-family: 'book antiqua', palatino, serif;font-size: 18pt\">\u201cThe straight line, a respectable optical illusion which ruins many a man\u201d<\/span><\/strong><\/em><\/span><br \/><span style=\"font-family: tahoma, arial, helvetica, sans-serif;font-size: 10pt;color: #808080\">\u00a0 -Victor Hugo-<\/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-spacer\" style=\"height: 100px\" aria-hidden=\"true\"><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\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>\u0dbd\u0d9a\u0dca\u0dc2 \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0daf\u0dd9\u0db1 \u0dbd\u0daf \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0d91\u0d9a\u0db8 \u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0dc4\u0ddd \u0daf\u0dd9\u0db4\u0dd0\u0dad\u0dca\u0dad\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd3\u0db8\u0da7 \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dad\u0dcf\u0dc0 \u0dc3\u0ddc\u0dba\u0dba\u0dd2.<\/p>\n","protected":false},"author":75,"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":[1023,3761,4163,4258,4170,4167,4257,4179,3879,4176,4152,4252,3792,3795,3931,4254,4178,4052,4256,4169,4180,4255,3977,3802,3885,4162,4249,4171,3875,4168,4174,3722,3800],"class_list":{"0":"post-12682","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-1023","13":"tag-combined-maths","14":"tag-coordinate-geometry-2","15":"tag-intersect","16":"tag-interstitial","17":"tag-learn-steer","18":"tag-opposite","19":"tag-opposite-side","20":"tag-parameter","21":"tag-peo","22":"tag-peo-maths","23":"tag-points","24":"tag-pure","25":"tag-pure-maths","26":"tag-rekhawa","27":"tag-relative","28":"tag-same-side","29":"tag-sanyuktha-ganithaya","30":"tag-segments","31":"tag-sequence","32":"tag-sign","33":"tag-straight","34":"tag-straight-lines","35":"tag-3802","36":"tag-3885","37":"tag---2","38":"tag-4249","39":"tag-4171","40":"tag-3875","41":"tag-4168","42":"tag-4174","43":"tag-3722","44":"tag-3800"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/12682"}],"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\/75"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=12682"}],"version-history":[{"count":200,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/12682\/revisions"}],"predecessor-version":[{"id":34970,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/12682\/revisions\/34970"}],"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=12682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=12682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=12682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}