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

According to question-


AP = BP


taking square on both sides, we get-


AP2 = BP2


⇒ (k-4)2 + (2-k)2 = (-1)2 + (2-5)2


[using distance formula, the distance between points (x1,y1) and (x2,y2) is equal to units.]


⇒ k2 - 8k + 16 + 4 + k2 - 4k = 1 + 9


⇒ 2k2 - 12k + 20 = 10


⇒ 2k2 - 12k + 10 = 0


⇒ 2(k2-6k + 5) = 0


⇒ (k2-5k-k + 5) = 0


⇒ k(k-5)-1(k-5) = 0


⇒ (k-1)(k-5) = 0


∴ k = 1 or k = 5


Thus, the value of k is 1 or 5.


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