Question

Find the value of k, if the point P (2, 4) is equidistant from the points A(5, k) and B (k, 7).

Find the value of k, if the points (5, k) and (k, 7) are equidistant from point (2, 4).

Answer 1

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.