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If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t. - Mathematics

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If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.

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Solution

Using distance formula, we have

AB = `sqrt((2-5)^2+(-2-2)^2)=sqrt(9+16)=5`

BC = `sqrt((-2-2)^2+(t+2)^2)=sqrt(t^2+4t+20)`

AC = `sqrt((-2-5)^2+(t-2)^2)=sqrt(t^2-4t+53) `

Now, it is given that ABC is right angled at B.

Using the Pythagorean theorem, we have

AB2 + BC2 = AC2

25+t2+4t+20=t24t+53            [From (1), (2) and (3)]

45+4t=4t+53

8t=8

t=1

Hence, the value of t is 1.

Concept: Distance Formula
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