Question

If A(5,2), B(2, -2) and C(-2, t) are the vertices of a right triangle with ∠B=90° , then find the value of t .

Answer 1

∵ ∠B = 90°

${\displaystyle \therefore A{C}^2=A{B}^2+B{C}^2}$

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

${\displaystyle \Rightarrow {\left(7\right)}^2+{(t-2)}^2={\left(3\right)}^2+{\left(4\right)}^2+{\left(4\right)}^2+{(t+2)}^2}$

${\displaystyle \Rightarrow 49+t^2-4t+4=9+16+16+t^2+4t+4}$

⇒ 8-4t=4t

⇒ 8t=8

⇒ t=1

Hence, t =1.