Question

if A(5,2), B(2,-2) and C (-2,t) are the vertices of right angled triangle with $\angle B={90}^0,$ then find the value of t.

Answer 1

Using Pythagoras theorem in right triangle ABC, we obtain

${AC}^2={AB}^2+{BC}^2$

$\Rightarrow {(5+2)}^2+{(2-t)}^2=\{{(5-2)}^2+{(2+2)}^2\}+\{{(2+2)}^2+{(-2-t)}^2\}$

$\Rightarrow 49+(4-4t+t^2)=(9+16)+(16+4+4t+t^2)$
$\Rightarrow t^2-4t+53=t^2+4t\times 45$
$\Rightarrow -8t=-8$
$\Rightarrow t=1$