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]
Solution:
It is given that A(0, 2) is equidistant from the points B(3, p) and C(p, 5).
∴ AB = AC
$\Rightarrow \sqrt{(3-0)^{2}+(p-2)^{2}}=\sqrt{(p-0)^{2}+(5-2)^{2}}$ (Distance formula)
Squaring on both sides, we get
$9+p^{2}-4 p+4=p^{2}+9$
$\Rightarrow-4 p+4=0$
$\Rightarrow p=1$
Thus, the value of p is 1.