# 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 . - Mathematics

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 .

#### Solution

∵ ∠B = 90°

∴ AC^2 = AB^2+BC^2

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

⇒(7)^2 +(t-2)^2 = (3)^2 +(4)^2 +(4)^2 + (t+2)^2

⇒ 49+t^2-4t+4=9+16+16+t^2+4t+4

⇒ 8-4t=4t

⇒ 8t=8

⇒ t=1

Hence, t =1.

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 21