If the points A(a, 0), B(0, b) and P(x, y) are collinear, using slopes, prove that

Question

Philoid · Accepted Answer

Given points are A(a,0),B(0,b) and P(x,y)

For three points to be collinear, the slope of all pairs must be equal, that is the slope of AB = slope of BP = slope of PA.

Slope of AB =

Slope of BP =

Slope of PA =

Now Slope of AB = BP = PA

Using the first two equality

Dividing the equation by “ab”, We get

Hence proved.