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

1.	If three points A(h, 0), P(a, b) and B(0, k) lie on a line, show that: \(\frac{a}{h}+\frac{b}{k} = 1.\)
Answer» If these three points lie on a line, the slope will be equal. So, slope of A(h, 0) and P(a, b) = Slope of A(h, 0) and B(0, k) Slope of AP = \(\Big(\frac{b-a}{a-h}\Big)\) Slope of AB = \(\Big(\frac{k-0}{0-h}\Big)\) Now, \(\Big(\frac{b-a}{a-h}\Big)\) = \(\Big(\frac{k-0}{0-h}\Big)\) \(\frac{b}{a-h}\) = \(-\frac{k}{h}\) bh = - ka + kh ak + bh = kh Dividing both sides by kh, we get, \(\frac{a}{h}\)+\(\frac{b}{k}\) = 1

If three points A(h, 0), P(a, b) and B(0, k) lie on a line, show that: \(\frac{a}{h}+\frac{b}{k} = 1.\)

Answer»

If these three points lie on a line, the slope will be equal.

So, slope of A(h, 0) and P(a, b) = Slope of A(h, 0) and B(0, k)

Slope of AP = \(\Big(\frac{b-a}{a-h}\Big)\)

Slope of AB = \(\Big(\frac{k-0}{0-h}\Big)\)

Now,

\(\Big(\frac{b-a}{a-h}\Big)\) = \(\Big(\frac{k-0}{0-h}\Big)\)

\(\frac{b}{a-h}\) = \(-\frac{k}{h}\)

bh = - ka + kh

ak + bh = kh

Dividing both sides by kh, we get,

\(\frac{a}{h}\)+\(\frac{b}{k}\) = 1