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Last updated at Feb. 3, 2020 by Teachoo

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Ex 10.1, 13 If three point (h, 0), (a, b) & (0, k) lie on a line, show that ๐/โ + ๐/๐ = 1 . Let points be A (h, 0), B (a, b), C (0, k) Given that A, B & C lie on a line Hence the 3 points are collinear โด Slope of AB = Slope of BC We know that Slope of a line through the points (x1, y1), (x2, y2) is m = (๐ฆ_2 โ ๐ฆ_1)/(๐ฅ_2 โ ๐ฅ_1 ) Slope of line AB through the points A(h, 0), B(a, b) Here x1 = h & y1 = 0 x2 = a & y2 = b Putting values m = (๐ โ 0)/(๐ โ โ) m = ๐/(๐ โ โ) Slope of line BC through the points B(a, b) & C(0, k) Here x1 = a & y1 = b x2 = 0 & y2 = k Putting values m = (๐ โ ๐)/(0 โ ๐) m = (๐ โ ๐)/(โ๐) Now, Slope of AB = Slope of BC ๐/(๐ โ โ) = (๐ โ ๐)/( โ ๐) โa(b) = (k โ b) (a โ h) โab = k(a โ h) โ b(a โ h) โab = ka โ kh โ ab + bh โab + ab = ka โ kh + bh 0 = ka + bh โ kh ka + bh = kh Dividing both sides by kh ๐๐/๐โ + ๐โ/๐โ = ๐โ/๐โ ๐/โ + ๐/k = 1 Hence proved

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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.