Question

Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).

Answer 1

Let the point is P(0, 2) which is equidistance from A(3, k) and B(k, 5) 

PA = PB

\(\sqrt{(3 - 0)^2 + (k - 2)^2}\) = \(\sqrt{(k - 0)^2 + (5 - 2)^2}\)

On squaring both sides, we get

9 + k² + 4 - 4k = k² + 9

- 4k = - 4

k = 1