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Ex 7.2, 9 Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts. Let the points that divide AB into 4 equal Parts be P1, P2 and P3 We know that AP1 = P1P2 = P2P3 = P3B Assuming AP1 = P1P2 = P2P3 = P3B = k Hence 𝐴𝑃2/𝑃2𝐵 = (𝐴𝑃1 + 𝑃1𝑃2)/(𝑃2𝑃3 +𝑃3𝐵) = ( 𝑘 + 𝑘)/(𝑘 + 𝑘) = ( 2𝑘)/2𝑘 = 1/1 = 1 : 1 Hence Point P2 divides AB into two equal parts AP2 & P2B Hence the coordinates of P2 are ((𝑥1 + 𝑥2)/2 ", " (𝑦1 +𝑦2)/2) = ((−2 + 2)/2 ", " (2 + 8)/2) = (0/2 ", " 10/2) = (0, 5) So, P2 (0, 5) Similarly, 𝐴𝑃1/𝑃1𝑃2 = ( 𝑘)/𝑘 = 1/1 = 1 : 1 Hence Point P1 divides AP2 into two equal parts Hence the coordinates of P1 are ((𝑥1 + 𝑥2)/2 ", " (𝑦1 +𝑦2)/2) = ((−2 +0)/2 "," (2 +5)/2) = ((−2)/2 ", " 7/2) = ("−1, " 7/2) So, P1 ("−1, " 𝟕/𝟐) Similarly, 𝑃2𝑃3/𝑃3𝐵 = ( 𝑘)/𝑘 = 1/1 = 1 : 1 Hence Point P3 divides P2B into two equal parts Hence the coordinates of P3 are ((𝑥1 + 𝑥2)/2 ", " (𝑦1 +𝑦2)/2) = ((0 + 2)/2 ", " (5 + 8)/2) = (2/2 ", " 13/2) = ("1, " 13/2) So, P3 ("1, " 𝟏𝟑/𝟐)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.