If three points (h, 0), (a, b) and (0, k) lie on a line, show that a/h + b/k = 1

Solution:

If three points A(h, 0), B (a, b) and C (0, k ) lie on a line (it means they are collinear), then

Slope of AB = Slope of BC

(b - 0)/(a - h) = (k - b)/(0 - a)

b/(a - h) = (k - b)/(-a)

-ab = (k - b)(a - h)

-ab = ka - kh - ab + bh

ka + bh = kh

On dividing both sides by kh , we obtain

ka/kh + bh/kh = kh/kh

a/h + b/k = 1

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.1 Question 13

If three points (h, 0), (a, b) and (0, k) lie on a line, show that a/h + b/k = 1

Summary:

If three points (h, 0), (a, b) and (0, k) lie on a line, then we have shown that a/h + b/k = 1