Question

Consider the following points on cartesian plane. A (1;2) BC3; 1) and CG-3; 4) prove that Points A, B and C are collinear. ​

Answer 1

Explanation:

Collinear points have the same gradient

find the gradient(slope) between AB first

`= (1 - 2)/(3 - 1) \\ = ( - 1)/(2)`

Find the one for BC

`= (4 - 1)/( - 3 - 3) \\ = (3)/( - 6) \\ = ( - 1)/(2)`

Find the gradient between AC now

`= (4 - 2)/( - 3 - 1) \\ = (2)/( - 4) \\ = ( - 1)/(2)`

YOUR LAST STATEMENT NOW WILL BE

POINTS A,B AND C ARE COLLINEAR SINCE THE GRADIENTS BETWEEN THEM IS THE SAME!!!