Question

By using slopes, show that the following points are collinear
$A(0,4)$, $B(2,10)$, $C(3,13)$

Answer 1

$A(0,4),B(2,10),C(3,13)$ are given points

$\therefore$ Slope of $AB=\frac{10-4}{2-0}$

$=\frac{6}{2}=3$ …….$\left(1\right)$

$\therefore$ Slope of $BC=\frac{13-10}{3-2}=3$ ……..$\left(2\right)$

$\therefore$ Slope of $CA=\frac{4-13}{0-3}=3$ ……..$\left(3\right)$

$\therefore$ From $\left(1\right),\left(2\right)$ & $\left(3\right)$

All points are collinear.