Question
If the point $A(0, 2)$ is equidistant from the points $B(3, p)$ and $C(p, 5)$, find P.
✓
Answer
The given points are $A(0, 2), B(3, p)$ and $C(p, 5)$.
$AB = AC \Rightarrow AB^2 = AC^2$
$\Rightarrow (3 - 0)^2 + (p - 2)^2 = (p - 0)^2 + (5 - 2)^2$
$\Rightarrow 9 + p^2 - 4p + 4 = P^2 + 9$
$\Rightarrow 4p = 4$
$ \Rightarrow p = 1$
Hence, $p = 1$
$AB = AC \Rightarrow AB^2 = AC^2$
$\Rightarrow (3 - 0)^2 + (p - 2)^2 = (p - 0)^2 + (5 - 2)^2$
$\Rightarrow 9 + p^2 - 4p + 4 = P^2 + 9$
$\Rightarrow 4p = 4$
$ \Rightarrow p = 1$
Hence, $p = 1$
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