Question

Show that the following points are collinear.

(1, 4), (3, -2) and (-1, 10)

Answer 1

$A(1,4),B(3,-2),C(-1,10)$

The condition for any three points to be collinear is :

$m_{AB}=m_{BC}$

Slope of $(x_1,y_1),(x_2,y_2)$ $=\frac{y_2-y_1}{x_2-x_1}$

$m_{AB}=\frac{-2-4}{3-1}=-3$

$m_{BC}=\frac{10-(-2)}{-1-3}=-3$

Hence they are collinear.