If the three points ( h , 0), ( a , b ) and ( 0, k ) lie on a straight line, then using the area of the triangle formula, show that where h, k ≠ 0.

Question

Philoid · Accepted Answer

Let A(h,0) B(am) and C (0, k) are the three points

Since the three points A(h,0) B (a, b) and C (0, k) lie on a straight line we can say that the three points are collinear.

So, area of triangle ABC = 0

Area of triangle =

x₁ = h, x₂ = a and x₃ = 0

y₁ = 0, y₂ = b and y₃ = k

⇒

⇒ 0 = hb + ak – kh

⇒ hab + ak = kh

Divided by (kh) on both sides we get

⇒

Hence proved.

If the three points (h, 0), (a, b) and (0, k) lie on a straight line, then using the area of the triangle formula, show that where h, k ≠ 0.