NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 13

Total: 74

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

= 1

Solution:

Let A(h, 0), B(a, b) and C(0, k) be the given collinear points.
∴ Slope of AB = Slope of BC
⇒

b−0

a−h

k−b

0−a

⇒

a−h

b−k

⇒ ab = (a – h) (b – k) ⇒ ab = ab – ak – hb + hk ⇒ ak + hb = hk
Dividing both sides by hk, we have

= 1

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