CBSE 2025 · Region 5 · Set 1 · Q29 · 3 marks
Find a relation between $\displaystyle x$ and y such that $\displaystyle \mathrm{P}(x, \mathrm{y})$ is equidistant from the points A$\displaystyle (3, 5)$ and B$\displaystyle (7, 1)$. Hence, write the coordinates of the points on $\displaystyle x$-axis and y -axis which are equidistant from points A and B .
Marking-scheme solution
\[\begin{aligned}
& P A=P B \Rightarrow P A^{2}=P B^{2} \\
& (x-3)^{2}+(y-5)^{2}=(x-7)^{2}+(y-1)^{2} \\
& \Rightarrow x-y=2
\end{aligned}
\]
∴ Required point on \(\displaystyle x\)-axis is \(\displaystyle (2,0)\)
& required point on \(\displaystyle y\)-axis is $\displaystyle (0, -2)$
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.