Question

Using section formula. show that the points $(-3,-1),(1,3)$ and $(-1,1)$ are collinear.

Answer 1

Given: $A(-3,-1),B(1,3),C(-1,1)$

$A(-3,-1)\equiv (x_2,y_2),B(1,3)\equiv (x_1,y_1)$

let $C$ divides $AB$ in ratio $k:1$

Here $m=k$ and $n=1$

so apply ratio formula we get

$[x=\left(\frac{m{x}_1+n{x}_2}{m+n}\right)]$ and $[y=\left(\frac{m{y}_1+n{y}_2}{m+n}\right)]$

$\frac{k-3}{k+1}=1$

and $\frac{3k-1}{k+1}=1$ .........(1)

by solving (1) equations we get $k=1$

therefore C divides AB in the ratio of $1:1$

so the three points are collinear