If three points (h, 0), (a, b) and (0, k) lies on a line, show that ah+bk=1
Let A(h, 0), B(a, b) and C(0, k) be three points lie on a line.
∴ Slope of AB=b−0a−h=ba−h
Slope of BC=k−b0−a=b−ka
Slope of AB = Slope of BC (given)
Dividing both sides by hk
akhk+bhhk=1 ⇒ ah+bk=1