Ex 10.1, 13

Transcript

Ex10.1, 13 If three point (h, 0), (a, b) and (0, k) lie on a line, show that 𝑎/ℎ + 𝑏/𝑘 = 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 = (𝑦2 − 𝑦1)/(𝑥2 − 𝑥1) –ab = ka – kh – ab + bh –ab + ab = ka – kh + bh 0 = ka + bh – kh ka + bh = kh Dividing both sides by kh 𝑘𝑎/𝑘ℎ + 𝑏ℎ/𝑘ℎ = 𝑘ℎ/𝑘ℎ 𝑎/ℎ + 𝑏/k = 1 Hence proved