Q22 of 77 Page 7

If the point P (k - 1, 2) is equidistant from the points A (3, k) and B (k,5), find the value of k.

Given: points A (3, k) and B (k,5).


To find: The value of k.


Formula Used:


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


Distance =


Explanation:


Coordinates of points are A(3, k), B(k, 5) and P(k - 1, 2)


Using distance formula =


⇒ PA = PB



On squaring both sides, we get
(k - 1 - 3)2 + (2 - k)2 = (k - 1 - k)2 + (2 - 5)2


(k - 4)2 + (2 - k)2 = ( - 1)2 + ( - 3)2


k2 - 8k + 16 + k2 - 4k + 4 = 1 + 9


k2 - 6k + 5 = 0


k2 - 5k - k + 5 = 0


k(k - 5) - 1(k - 5) = 0


(k - 5) (k - 1) = 0


k = 1, 5


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