Question

Show that the points $A(-5,1),B(5,5)$ and $C(10,7)$ are collinear.

Answer 1

Given points are

$A(-5,1),B(5,5)$ and $C(10,7)$

We know that

$ABC=\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|$

Here $A(-5,1),B(5,5),C(10,7)$

$x_1,y_1$ $x_2,y_2$ $x_3,y_3$

$ABC=\frac{1}{2}\left|\right(-5\left)\right(5-7)+6(7-1)+10(1-5\left)\right|$

$=\frac{1}{2}\left|\right(-5\left)\right(-2)+5(6)+10(-4\left)\right|$

$=\frac{1}{2}|10+30-40|$

$=\frac{1}{2}|40-40|$

$=\frac{1}{2}\left|0\right|=0$

$\therefore$ Given points are collinear.