Question

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. [CBSE 2014]

Answer 1

The given points are A(0, 2), B(3, p) and C(p, 5).
$$\begin{gathered} AB=AC\Rightarrow A{B}^2=A{C}^2 \\ \Rightarrow {\left(3-0\right)}^2+{\left(p-2\right)}^2={\left(p-0\right)}^2+{\left(5-2\right)}^2 \\ \Rightarrow 9+p^2-4p+4=p^2+9 \\ \Rightarrow 4p=4\Rightarrow p=1 \end{gathered}$$
Hence, p = 1.