Question

If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find the value of p. [CBSE 2012, 2013]

Answer 1

It is given that A(0, 2) is equidistant from the points B(3, p) and C(p, 5).

∴ AB = AC

$\Rightarrow \sqrt{{\left(3-0\right)}^2+{\left(p-2\right)}^2}=\sqrt{{\left(p-0\right)}^2+{\left(5-2\right)}^2}$ (Distance formula)

Squaring on both sides, we get

$$\begin{gathered} 9+p^2-4p+4=p^2+9 \\ \Rightarrow -4p+4=0 \\ \Rightarrow p=1 \end{gathered}$$

Thus, the value of p is 1.