Question

Show that the points are collinear $(-5,1)(5,5)(10,7)$

Answer 1

Let the three collinear points be $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$

The condition of collinearity is $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$

Here, the given points are $(-5,1)$, $(5,5)$ and $(10,7)$

$-5(5-7)+5(7-1)+10(1-5)=-5(-2)+5\left(6\right)+10(-4)=10+30-40=0$

Hence, points $(-5,1)$, $(5,5)$ and $(10,7)$ are collinear