Q17 of 66 Page 7

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.(CBSE 2014)

Distance between two points (x1,y1) and (x2,y2) is given by


√ (x1-x2)2 + (y1-y2)2


Length of AC = √ (5-(-2))2 + (2-t)2

= √ 49 + (t-2)2


Length of BC = √ (2-(-2))2 + (-2-t)2

= √16 + (t + 2)2


Length of AB = √ (5-2)2 + (2-(-2))2

= √9 + 16 = √25 = 5


ABC is right angled at B,


AC2 = AB2 + BC2


⇒ 49 + (2-t)2 = 16 + (t + 2)2 + 25


⇒ (t2 + 4-4t) = (t2 + 4t + 4) + (25 + 16-49)


⇒ -4t = 4t-8


⇒ 8t = 8


⇒ t = 1

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