Check sibling questions

Ex 10.1, 13 - If points (h, 0), (a, b), (0, k) lie on a line

Ex 10.1, 13 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.1, 13 - Chapter 10 Class 11 Straight Lines - Part 3


Transcript

Ex 10.1, 13 If three point (h, 0), (a, b) & (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 = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_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 = (𝑏 − 0)/(𝑎 − ℎ) m = 𝑏/(𝑎 − ℎ) 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 = (𝑘 − 𝑏)/(0 − 𝑎) m = (𝑘 − 𝑏)/(−𝑎) Now, Slope of AB = Slope of BC 𝑏/(𝑎 − ℎ) = (𝑘 − 𝑏)/( − 𝑎) –a(b) = (k – b) (a – h) –ab = k(a – h) – b(a – h) –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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.