If A(5,2), B(2,-2) and C(-2,t) are the vertices of a right angled triangle with angle B=90°, then find the value of t
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(AB)2 + (BC)2 =(AC)2
(x2 - x1)2 + (y2 - y1)2 + (x2 - x1)2 + (y2 - y1)2= (x2 - x1)2 + (y2 - y1)2
(2 - 5)2 + (-2 -2)2 + (-2 -2)2 + (t +2)2 = (-2 -5)2 + (t - 2)2
(-3)2 + (-4)2 + (-4)2 = (t)2 + (2)2 + 4t = (-7)2+ (t)2 +(2)2 - 4t
9 + 16 + 16 + t2 + 4 + 4t = 49 + t2 + 4 - 4t
-8 = -4t - 4t
8 = 8t
or t = 8/8
or t = 1
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(AB)2 + (BC)2 =(AC)2
(x2 - x1)2 + (y2 - y1)2 + (x2 - x1)2 + (y2 - y1)2= (x2 - x1)2 + (y2 - y1)2
(2 - 5)2 + (-2 -2)2 + (-2 -2)2 + (t +2)2 = (-2 -5)2 + (t - 2)2
(-3)2 + (-4)2 + (-4)2 = (t)2 + (2)2 + 4t = (-7)2+ (t)2 +(2)2 - 4t
9 + 16 + 16 + t2 + 4 + 4t = 49 + t2 + 4 - 4t
-8 = -4t - 4t
8 = 8t
or t = 8/8
or t = 1
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