Question

The points $A(0,3),B(-2,a)$ and $C(-1,4)$ are the vertices of a right angled triangle at $A$ , find the value of $a.$

Answer 1

Solution -

$A(0,3),B(-2,a),C(-1,a)$ is right angles triangle at A

$AB\perp AC$

Slope of AB $\times$ slope of AC = -1

$\frac{a-3}{-2}\times \frac{1}{-1}=-1$

$a-3=-2$

$a=1$