If the three points A(h, k), B(x 1 , y 1 ) and C(x 2 , y 2 ) lie on a line then show that (h – x 1 )(y 2 – y 1 ) = (k – y 1 )(x 2 – x).

Question

Philoid · Accepted Answer

For the lines to be in a line, the slope of the adjacent lines should be the same.

Given points are A(h,k),B(x₁,y₁) and C(x_2,y₂)

So slope of AB = BC = CA

Slope of AB =

Slope of BC =

Slope of CA =

=

Now Cross multiplying the first two equality,

Hence proved.

If the three points A(h, k), B(x1, y1) and C(x2, y2) lie on a line then show that (h – x1)(y2 – y1) = (k – y1)(x2 – x).