Question

State whether True or False

(-1, 8), (9, -2), (3,4) are collinear points.

Answer 1

When three points $A,B$ and $C$ are collinear, slope of line joining any two points (say $AB$) $=$ slope of line joining any other two points (say $BC$).
Slope of the line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ $=$ $\frac{y_2-y_1}{x_2-x_1}$
Slope of the line passing through $(-1,8)$ and $(9,-2)=\frac{-2-8}{9-(-1)}=\frac{-10}{10}=-1$.
Slope of the line passing through $(9,-2)$ and $(3,4)=\frac{4-(-2)}{3-9}=\frac{6}{-6}=-1$
Slope of both lines are same. Hence the given points are collinear.