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Question
Find the value of k, if the point P (2, 4) is equidistant from the points A(5, k) and B (k, 7).
Solution
It is given that point P (2, 4) is equidistant from the points A (5, k) and B (k, 7).
∴ AP = BP
On squaring both sides, we get
AP2 = BP2
⇒ (2 − 5)2 + (4 − k)2 = (2 − k)2 + (4 − 7)2 [Using distance formula]
⇒ (−3)2 + 42 − (2 × 4 × k) + k2 = 22 − (2 × 2 × k) + k2 + (− 3)2
⇒ 9 + 16 − 8k + k2 = 4 − 4k + k2 + 9
⇒ k2 − 8k + 25 = k2 − 4k + 13
⇒ k2 − k2 − 8k + 4k = 13 − 25
⇒ − 4k = − 12
`rArr k=(-12)/-4=3`
Hence, the value of k is 3.
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