If point (x, y) is equidistant from points (7,1) and (3,5), show … - Vidyadip

Question

If point $(x, y)$ is equidistant from points $(7,1)$ and $(3,5)$, show that $y=x-2$.

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Answer

Let point $\mathrm{P}(x, y)$ be equidistant from points $\mathrm{A}(7,1)$ and $\mathrm{B}(3,5)$
$
\begin{aligned}
\therefore \mathrm{AP} & =\mathrm{BP} \\
\therefore \mathrm{AP}^2 & =\mathrm{BP}^2 \\
\therefore(x-7)^2+(y-1)^2 & =(x-3)^2+(y-5)^2 \\
\therefore x^2-14 x+49+y^2-2 y+1 & =x^2-6 x+9+y^2-10 y+25 \\
\therefore-8 x+8 y & =-16 \\
\therefore x-y & =2 \\
\therefore y & =x-2
\end{aligned}
$

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