Ex 10.1, 13 - Chapter 10 Class 11 Straight Lines

Transcript

Ex10.1, 13 If three point (h, 0), (a, b) and (0, k) lie on a line, show that / + / = 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 Slope of AB = Slope of BC We know that slope of a line through the points (x1, y1)(x2, y2)is m = ( 2 1)/( 2 1) ab = ka kh ab + bh ab + ab = ka kh + bh 0 = ka + bh kh ka + bh = kh Dividing both sides by kh / + / = / / + /k = 1 Hence proved