Ex 10.1, 13 - If points (h, 0), (a, b), (0, k) lie on a line - Collinearity of 3 points by sliope

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Ex10.1, 13 If three point (h, 0), (a, b) and (0, k) lie on a line, show that ๐‘Ž/โ„Ž + 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 โˆด Slope of AB = Slope of BC We know that slope of a line through the points (x1, y1)(x2, y2)is m = (๐‘ฆ2 โˆ’ ๐‘ฆ1)/(๐‘ฅ2 โˆ’ ๐‘ฅ1) โ€“ab = ka โ€“ kh โ€“ ab + bh โ€“ab + ab = ka โ€“ kh + bh 0 = ka + bh โ€“ kh ka + bh = kh Dividing both sides by kh ๐‘˜๐‘Ž/๐‘˜โ„Ž + ๐‘โ„Ž/๐‘˜โ„Ž = ๐‘˜โ„Ž/๐‘˜โ„Ž ๐‘Ž/โ„Ž + ๐‘/k = 1 Hence proved

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