Question

If the points (a, 0), (0, b) and (1, 1) are collinear, prove that a + b = ab

Answer 1

Here, (a, 0), (0, b) and (1, 1) are collinear

The condition given that three points to be collinear, the area of the triangle formed by these points will be zero. As we know that, vertices of a triangle are (x₁, y₁), (x₂, y₂) and (x₃, y₃), then the area of the triangle is given by,

On substituting the value from above

On expanding along R₁

⇒ a + b = ab

Hence Proved