Question

Prove that $A(2,1),B(0,3)$ and $C(-2,1)$ are the above vertices of an isoceles right triangle. Hence find the coordinates of a point D, if ABCD is a square

Answer 1

REF.Image.

A(2,1) B(0,3) C(-2,1)

$AB=\sqrt{2^2}+2^2=2\sqrt{2}$

$BC=\sqrt{2^2+2^2}=2\sqrt{2}$

$CA=\sqrt{4^2}=4$ Hence it isoceles $\angle$ angle $△$

$A{B}^2+B{C}^2=C{A}^2$

$0(\frac{-2+2}{2},\frac{1+1}{2})=0(0,1)$

$\frac{x+0}{2}=0\Rightarrow x=0$

$\frac{y+3}{2}=1\Rightarrow y=-1$

point D (0,-1)