Q20 of 77 Page 7

Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, - 1), (1, 3) and (x, 8) respectively.

Given: PQ = QR


P, Q and R are (6, - 1), (1, 3) and (x, 8)


To find: The value of x.


Formula Used:


The distance between the points (x1, y1) and (x2,y2) is:


Distance =


Explanation:


Coordinates are P (6, - 1), Q(1, 3) and R(x, 8)


Using distance formula =


⇒ PQ = QR



On squaring both sides, we get
(1 - 6)2 + (3 + 1)2 = (x - 1)2 + (8 - 3)2


25 + 16 = x2 - 2x + 1 + 25


x2 - 2x – 15 = 0


On solving above equation, we get


x2 - 5x + 3x – 15 = 0


x(x - 5) + 3(x - 5) = 0


(x + 3) (x - 5) = 0


x = - 3


x = 5


Therefore x = - 3, 5


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