Question

The points $A(0,3)$ , B(-2,y) and (-1,4) are the vertices of a $\Delta ABC$ right-angled at A.Find the value of y.

Answer 1

$\begin{array}{c}B{C}^2=A{C}^2+A{B}^2\\ {\left(\sqrt{{\left(-2+1\right)}^2+{\left(y-4\right)}^2}\right)}^2={\left(\sqrt{{\left(-1\right)}^2+{\left(1\right)}^2}\right)}^2+{\left(\sqrt{{\left(-2\right)}^2+{\left(-3+y\right)}^2}\right)}^2\\ =1+{\left(y-4\right)}^2=2+4+{\left(-3+y\right)}^2\\ =y^2+16-8y+1=2+4+9+y^2-6y\\ =2y+15-17=0\\ =y=\frac{2}{2}=1\end{array}$