Q8 of 184 Page 10

If A = (6, 1), B = (1, 3) and C = (x, 8), find the value of x such that AB = BC.

Given points are A(6, 1), B(1, 3) and C(x, 8). We need to find the value of x such that AB = BC.



We know that the distance between the points (x1, y1) and (x2, y2) is


⇒ AB = BC


⇒ AB2 = BC2


⇒ (6 - 1)2 + (1 - 3)2 = (1 - x)2 + (3 - 8)2


⇒ (5)2 + (- 2)2 = (1 - x)2 + (- 5)2


⇒ 25 + 4 = 1 - 2x + x2 + 25


⇒ x2 - 2x - 3 = 0


⇒ x2 - 3x + x - 3 = 0


⇒ x(x - 3) + 1(x - 3) = 0


⇒ (x + 1)(x - 3) = 0


⇒ x + 1 = 0 (or) x - 3 = 0


⇒ x = - 1 (or) x = 3


∴ The values of x are - 1 or 3.


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