If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find the value of p.

Question

Philoid · Accepted Answer

The figure will be drawn as

Since, point A is equidistant from points B and C. We can write in the form,

BA = AC …(i)

Now, length BA =

And length AC =

Substituting lengths BA and AC in equation (i), we get

Squaring both sides, we get

(3 – 0)² + (p – 2)² = (0 – p)² + (2 – 5)²

⇒ 9 + p² + 4 – 4p = p² + 9

⇒ 4p = 4

⇒ p = 1

Hence, the value of p is 1.