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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 2 · Set 1 · Q28
If Q (0,1) is equidistant from P (5,-3) and R ( x, 6), find the values of x.
If $\displaystyle \mathrm{Q}(0,1)$ is equidistant from $\displaystyle \mathrm{P}(5,-3)$ and $\displaystyle \mathrm{R}(\mathrm{x}, 6)$, find the values of x.
Marking-scheme solution
\[\begin{aligned}
& P Q=Q R \Rightarrow P Q^{2}=Q R^{2} \\
& (5-0)^{2}+(-3-1)^{2}=(x-0)^{2}+(6-1)^{2} \\
& \Rightarrow 25+16=x^{2}+25 \\
& \Rightarrow x^{2}=16 \\
& \Rightarrow x=4, x=-4
\end{aligned}
\]
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