Question

By using slopes, show that the following points are collinear
$L(2,5)$, $M(5,7)$, $N(8,9)$

Answer 1

Here $L\equiv (2,5),M\equiv (5,7),N(8,9)$

$\therefore$ Slope of LM =$\frac{7-5}{5-2}=\left[\frac{2}{3}\right]$_____$\left(1\right)$

$\therefore$ Slope of NM = $\frac{9-7}{8-5}=\left[\frac{2}{3}\right]$_____$\left(2\right)$

$\therefore$ Slope of NL= $\frac{5-9}{2-8}=\frac{-4}{-6}$

$=\frac{2}{3}$______$\left(3\right)$

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

$\therefore$ points are collinear.