{"id":10899,"date":"2021-05-25T14:06:30","date_gmt":"2021-05-25T08:36:30","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=10899"},"modified":"2021-10-14T01:03:51","modified_gmt":"2021-10-13T19:33:51","slug":"03-02-07","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/03-02-07\/","title":{"rendered":"03.02.07 &#8211; \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0d9a  \u0dc3\u0dd2\u0da7 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a\u0da7 \u0d87\u0dad\u0dd2 \u0dbd\u0db8\u0dca\u0db7 \u0daf\u0dd4\u0dbb \u0dc3\u0dd9\u0dc0\u0dd3\u0db8"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/uc?id=1V7RWunm1xD6vLeD8lCn1S2Xo2hhlaiEz&amp;export=download\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>A (x<sub>0,<\/sub> y<sub>0<\/sub>) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0dc3\u0dd2\u0da7 ax+by+c= 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dd2 \u0dbd\u0db8\u0dca\u0db7 \u0daf\u0dd4\u0dbb \u0dc3\u0dbd\u0d9a\u0db8\u0dd4.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"279\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-3.png\" alt=\"\" class=\"wp-image-12014\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-3.png 274w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-3-150x153.png 150w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>A (x<sub>0<\/sub>, y<sub>0<\/sub>) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc4\u0dbb\u0dc4\u0dcf ax+by+c= 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dd2 \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0d95\u0db1\u0dd1\u0db8 P (x, y) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0dbd\u0d9a\u0dd4\u0dab\u0dd4 \u0d9a\u0dbb\u0db8\u0dd4.<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\text{(AP\u00a0\u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba)\u00a0(ax+by+c=\u00a00\u00a0\u0dc3\u0dbb\u0dbd\u00a0\u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda\u00a0\u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba)}&amp;=&amp;-1\\\\\\left(\\frac{y-y_0}{x-x_0}\\right)\\left(\\frac{-a}b\\right)\\;&amp;=&amp;\\;-1\\end{array}&lt;\/p&gt;\n\n\n\n&lt;p class=&quot;has-text-align-center&quot;&gt;[latex]\\frac{y-y_0}b\\;=\\;\\frac{x-x_0}a\\left(=t\\;\\text{\u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4}\\;\\right)<\/span><\/p>\n\n\n\n<p class=\"has-text-align-left\">\u0db8\u0dd9\u0dc4\u0dd2 t \u0dba\u0db1\u0dd4 \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0db4\u0dbb\u0db8\u0dd2\u0dad\u0dd2\u0dba\u0d9a\u0dd2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{y-y_0}b\\;=\\;t\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;y\\;=\\;y_0+bt<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{x-x_0}a\\;=\\;t\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;x\\;=\\;x_0+at<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\">P \u2261 {(x<sub>0<\/sub>+at), (y<sub>0 <\/sub>+bt)}<\/p>\n\n\n\n<p>&nbsp;A \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0dc3\u0dd2\u0da7 ax + by + c = 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0daf\u0dd2 \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dba\u0dda \u0d85\u0da9\u0dd2\u0dba B \u0daf, B \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0dbb\u0dd6\u0db4 \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0dba t<sub>0 <\/sub>\u0dbd\u0dd9\u0dc3\u0daf \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<p class=\"has-text-align-center\">B= {(x<sub>0<\/sub>+at<sub>0<\/sub>), (y<sub>0<\/sub>+bt<sub>0<\/sub>)}<\/p>\n\n\n\n<p>\u0db8\u0dd9\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0db8\u0d9c\u0dd2\u0db1\u0dca ax+by+c= 0&nbsp;\u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}a(x_0+at_0)+b(y_0+bt_0)+c=0\\\\(ax_0+by_0+c)+a^2t_0+b^2t_0=0\\\\{(ax_0+by_0+c)}+(a^2+b^2)\\;t_0=0\\\\t_0=-\\frac{(ax_0+by_0+c)}{(a^2+b^2)}\\end{array}<\/span>\n\n\n\n<p>A \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0dc3\u0dd2\u0da7 ax+by+c= 0&nbsp; &nbsp;\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0daf\u0dd2 \u0dbd\u0db8\u0dca\u0db7 \u0daf\u0dd4\u0dbb d \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}d^2&amp;=&amp;\\left[(x_0+at_0\\;)-x_0\\right]^2+\\left[(y_0+bt_0)-y_0\\right]^2\\&amp;&amp;\\\\d^2&amp;=&amp;t_0^2\\left(a^2+b^2\\right)\\\\&amp;&amp;\\\\d^2&amp;=&amp;\\left[-\\frac{\\left(ax_0+by_0+c\\right)}{\\left(a^2+b^2\\right)}\\right]^2\\left(a^2+b^2\\right)\\\\&amp;&amp;\\\\d&amp;=&amp;\\frac{\\left|ax_0+by_0+c\\right|}{\\sqrt{\\left(a^2+b^2\\right)}}\\;;\\;d&gt;0\\end{array}<\/span>\n\n\n\n<p>\u0d8b\u0daf\u0dcf :(1.) t \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7 x=t<sup>2<\/sup>, y=2t \u0dc0\u0db1 p\u2261 (x, y) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0dc3\u0dd2\u0da7 l\u2261x+3y+8=0 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dd2 \u0daf\u0dd4\u0dbb \u0d85\u0dc0\u0db8\u0dba\u0d9a\u0dca \u0dc0\u0db1 P \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"311\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-235.png\" alt=\"\" class=\"wp-image-16033\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-235.png 354w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-235-300x264.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-235-150x132.png 150w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/figure><\/div>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; P \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0dc3\u0dd2\u0da7 l=0 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dd2 \u0d9a\u0dd9\u0da7\u0dd2\u0dad\u0db8 \u0daf\u0dd4\u0dbb d \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}d&amp;=&amp;\\frac{\\left|\\mathrm t^2+3\\left(2\\mathrm t\\right)+8\\right|}{\\sqrt{1^2+3^2}}\\\\d&amp;=&amp;\\frac{\\left|\\left(\\mathrm t+3\\right)^2-1\\right|}{\\sqrt{10}}\\end{array}<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d \u0d85\u0dc0\u0db8 \u0dc0\u0db1\u0dd4\u0dba\u0dda,&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;t = -3&nbsp;&nbsp;&nbsp; \u0dc0\u0db1 \u0dc0\u0dd2\u0da7\u0daf\u0dd3\u0dba.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\therefore<\/span>\u0d86\u0dc3\u0db1\u0dca\u0db1\u0dad\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a&nbsp;&nbsp; (9, -6) \u0dc0\u0dda<\/p>\n\n\n\n<p><strong>\u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb<\/strong> <strong>\u0dc3\u0dbb\u0dbd<\/strong> <strong>\u0dbb\u0dda\u0d9b\u0dcf<\/strong> <strong>\u0d85\u0dad\u0dbb<\/strong> <strong>\u0daf\u0dd4\u0dbb<\/strong> <strong>\u0dc3\u0dd9\u0dc0\u0dd3\u0db8<\/strong><strong>.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>ax+by+c=0 \u0dc4\u0dcf ax+by+c\u2019=o \u0dba\u0db1 \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0d85\u0dad\u0dbb \u0daf\u0dd4\u0dbb \u0dc3\u0dd9\u0dc0\u0dd3\u0db8.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"287\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-5.png\" alt=\"\" class=\"wp-image-12080\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-5.png 274w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-5-150x157.png 150w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>ax + by + c\u2019 = 0 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad (x<sub>0<\/sub>, y<sub>0<\/sub>) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc3\u0dbd\u0d9a\u0db8\u0dd4. \u0db8\u0dd9\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0dc3\u0dd2\u0da7&nbsp; ax + by + c = 0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0d87\u0dad\u0dd2 \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0daf\u0dd4\u0dbb \u0dc0\u0db1 d \u0daf\u0dd3 \u0d87\u0dad\u0dd2&nbsp; \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0d85\u0dad\u0dbb \u0daf\u0dd4\u0dbb \u0dc0\u0dda .<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm d=\\frac{\\left|{\\mathrm{ax}}_0+{\\mathrm{by}}_0+\\mathrm c\\right|}{\\sqrt{\\mathrm a^2+\\mathrm b^2}}<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(x<sub>0, <\/sub>y<sub>0<\/sub>) \u0db8\u0d9c\u0dd2\u0db1\u0dca&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;ax+by+c\u2019=0 \u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}ax_0+by_0+c&#039;&amp;=&amp;0\\\\ax_0+by_0&amp;=&amp;-c\u2019\\end{array}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\mathrm d\\;=\\;\\frac{\\left|\\mathrm c-\\mathrm c&#039;\\right|}{\\sqrt{\\mathrm a_2+\\mathrm b_2}}\\;\\;\\;\\;<\/span><\/p>\n<\/div><\/div>\n\n\n\n<p>\u0d8b\u0daf\u0dcf :(1)&nbsp;&nbsp;&nbsp; 4x - 3y \u2013 4 = 0 \u0dc3\u0dc4 \u0db8\u0dd9\u0db8 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dc0 (3 , -2) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba&nbsp;&nbsp; \u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0&nbsp; \u0d85\u0dad\u0dbb&nbsp; \u0daf\u0dd4\u0dbb \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1 .<\/p>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"296\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-6.png\" alt=\"\" class=\"wp-image-12081\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-6.png 292w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/03\/image-6-150x152.png 150w\" sizes=\"(max-width: 292px) 100vw, 292px\" \/><\/figure><\/div>\n\n\n\n<p>(3, -2) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba l<sub>1 <\/sub>= 0 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0db8\u0dad \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca \u0d91\u0db8 \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0dda.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4(3) \u20133( -2) +k =0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;k= -18<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; l<sub>1<\/sub>=0 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba 4x -3y -18=0 \u0dc0\u0dda.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\mathrm d\\;&amp;=&amp;\\;\\frac{\\left|\\mathrm c-\\mathrm c&#039;\\right|}{\\sqrt{\\mathrm a_2+\\mathrm b_2}}\\\\\\mathrm d\\;&amp;=&amp;\\;\\frac{\\left|-18-\\left(-4\\right)\\right|}{\\sqrt{3^2+(-2)^2}}\\\\\\mathrm d\\;&amp;=&amp;\\;\\frac{14}5\\end{array}<\/span><\/p>\n\n\n\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\n\n\n\n<\/span><\/p>\r\n<p class=\"has-text-align-center has-background\" style=\"background-color: #272062;text-align: center\"><span style=\"color: #ffffff\"><em><strong><span style=\"font-family: 'book antiqua', palatino, serif;font-size: 18pt\">\u201cMathematics is the most beautiful and most powerful creation of the human spirit.\u201d<\/span><\/strong><\/em><\/span><br \/><span style=\"font-family: tahoma, arial, helvetica, sans-serif;font-size: 10pt;color: #808080\">-Stefan Banach<\/span><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\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><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>\n<\/div>\n\n\n\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\n\n\n\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\n\n\n\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0db4\u0dbb\u0dcf\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0d9a \u0dc3\u0dd2\u0da7 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a\u0da7 \u0d87\u0dad\u0dd2 \u0dbd\u0db8\u0dca\u0db6 \u0daf\u0dd4\u0dbb \u0dc3\u0dd9\u0dc0\u0dd3\u0dd2\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":[3915,3886,3803,3922,3918,3919,3920,3921,3916,3917,3880,3914,3799,3873,3798,3924,3885,3876,3875,3926,3911,3909,3912,3923,3910,3800,3913,3925],"class_list":{"0":"post-10899","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-co-ordinates","13":"tag-coordinates","14":"tag-gradient","15":"tag-gradient-of-a-straight-line","16":"tag-paralal-line","17":"tag-paralel-lines","18":"tag-paralel-straight-line","19":"tag-paralel-straight-lines","20":"tag-parallel-lines","21":"tag-parallel-straight-lines","22":"tag-perpendicular","23":"tag-perpendicular-distance","24":"tag-sarala-rekawa","25":"tag-sarala-rekhawa","26":"tag-straight-line","27":"tag-3924","28":"tag-3885","29":"tag-3876","30":"tag-3875","31":"tag-3926","32":"tag-3911","33":"tag-3909","34":"tag-3912","35":"tag-3923","36":"tag-3910","37":"tag-3800","38":"tag-3913","39":"tag-3925"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/10899"}],"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=10899"}],"version-history":[{"count":29,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/10899\/revisions"}],"predecessor-version":[{"id":32648,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/10899\/revisions\/32648"}],"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=10899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=10899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=10899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}