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Question

If three points (h, 0), (a, b) and (0, k) lies on a line, show that ah+bk=1


Solution

Let A(h, 0), B(a, b) and C(0, k) be three points lie on a line.

    Slope of AB=b0ah=bah

Slope of BC=kb0a=bka

Slope of AB = Slope of BC (given)

  bah=bkaab=abakbh+hk

   ak+bh=hk

Dividing both sides by hk

akhk+bhhk=1    ah+bk=1

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