Question

If a(5,2), b(2,-2) and c(-2,t) are the vertices ofa right triangle with angle b=90°.Then find the value of t.

Answer 1

by pythogoras theorem,

ac^2=ab^2+bc^2

(5+2)^2+(2-t)^2=(5-2)^2+(2+2)^2+(2+2)^2+(-2-t)^2

49+(2-t)^2=9+16+16+(2+t)^2

49+4+t^2-4t=41+4+t^2+4t

8-4t=4t

t=1