Question

If A(5, 2), B(2, -2) and C(-2, t) are the vertices of right angled triangle with
angleB = 90°, then value of t
​

Answer 1

It is given that angleB is 90°

Applying pythagoras theorem, we get

(AB)^2+(BC)^2=(AC)^2

(AB)^2 = [(5-2)^2+(2+2)^2] = (9+16)=25

(BC)^2 = [(2+2)^2+(-2-t)^2]

= 16+ 4 + 4t + t^2

= t^2 + 4t + 20

(AC)^2=[(5+2)^2 +(2-t)^2]

= 49 + 4 + t^2 -4t

= t^2 -4t + 53

solving these equations...we get

8t = 8

t = 1

value of t is 1