If A(5,2),B(2,_2)and C(-2,t) are the vertecal of a right angled triangle with/_B=90′,then find the value of t.

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Applying Pythagoras theorem, we have,

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 + 4 – 4t + t^2] = [9 + 16] + [16 + 4 + 4t + t^2] 53 – 4t = 45 – 4t 8t = 8 t = 1

Hence, the value of t is 1.

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