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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 .
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.
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