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If the point $\mathrm{A}(0,2)$ is equidistant from the points $\mathrm{B}(3, \mathrm{p})$ and $\mathrm{C}(\mathrm{p}, 5)$, find $\mathrm{p}$.
If the point $\mathrm{A}(0,2)$ is equidistant from the points $\mathrm{B}(3, \mathrm{p})$ and $\mathrm{C}(\mathrm{p}, 5)$, find $\mathrm{p}$.
CBSE | Class 10 | Coordinate Geometry | Exercise 16.4 | Maths | RS Aggarwal
If the point $\mathrm{A}(0,2)$ is equidistant from the points $\mathrm{B}(3, \mathrm{p})$ and $\mathrm{C}(\mathrm{p}, 5)$, find $\mathrm{p}$.

The given ports are $A(0,2), B(3, p)$ and $C(p, 5)$.

$\begin{aligned}
&A B=A C \Rightarrow A B^{2}=A C^{2} \\
&\Rightarrow(3-0)^{2}+(p-2)^{2}=(p-0)^{2}+(5-2)^{2} \\
&\Rightarrow 9+p^{2}-4 p+4=p^{2}+9 \\
&\Rightarrow 4 p=4 \Rightarrow p=1 \\
&\text { Hence, } p=1
\end{aligned}
$

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