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Last updated at May 29, 2018 by Teachoo

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Ex 7.2 , 9 Find the coordinates of the points which divide the line segment joining A(โ 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 ๐ด๐2/๐2๐ต = (๐ด๐1 + ๐1๐2)/(๐2๐3 +๐3๐ต) = ( ๐ + ๐)/(๐ + ๐) = ( 2๐)/2๐ = 1/1 = 1 : 1 Hence Point P2 divides AB into two equal parts AP2 & P2B Hence the coordinates of P2 are ((๐ฅ1 + ๐ฅ2)/2, (๐ฆ1 +๐ฆ2)/2) = ((โ2 + 2)/2, (2 + 8)/2) = (0/2, 10/2) = (0, 5) So, P2(0, 5) Similarly, ๐ด๐1/๐1๐2 =( ๐)/๐ = 1/1 = 1 : 1 Hence Point P1 divides AP2 into two equal parts Hence the coordinates of P1 are ((๐ฅ1 + ๐ฅ2)/2, (๐ฆ1 +๐ฆ2)/2) = ((โ2 +0)/2, (2 +5)/2) = ((โ2)/2, 7/2) = (โ1, 7/2) So, P1 (โ1, 7/2) Similarly, ๐2๐3/๐3๐ต =( ๐)/๐ = 1/1 = 1 : 1 Hence Point P3 divides P2B into two equal parts Hence the coordinates of P3 are ((๐ฅ1 + ๐ฅ2)/2, (๐ฆ1 +๐ฆ2)/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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.