if A(5,2), B(2,-2) and C(-2,t) are vertices of angle with angle B=90 findthe value of t - Maths - Coordinate Geometry

Question

if A(5,2), B(2,-2) and C(-2,t) are vertices of angle with angle
B=90 findthe value of t

Varun.Rawat · Accepted Answer

We have,A5, 2; B2, -2; C-2, t as the given points of∆ABC in which ∠B = 90°Now, AC2 = AB2 + BC2    Pythagoras theorem⇒-2-52 + t-22 =2-52 + -2-22 +-2-22 + t+22⇒49 + t2 + 4 - 4t = 9 + 16 + 16 + t2 + 4 + 4t⇒53 - 4t = 45 + 4t⇒8t = 8⇒t = 1