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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 5 · Set 1 · Q21
The line segment joining the points $\displaystyle \mathrm{A}(4,-5)$ and $\displaystyle \mathrm{B}(4,5)$ is divided by the point P such that $\displaystyle \mathrm{AP}: \mathrm{AB}=2: 5$. Find the coordinates of P .Point P(x, y) is equidistant from points A$\displaystyle (5, 1)$ and B$\displaystyle (1, 5)$. Prove that $\displaystyle \mathrm{x}=\mathrm{y}$.
The line segment joining the points $\displaystyle \mathrm{A}(4,-5)$ and $\displaystyle \mathrm{B}(4,5)$ is divided by the point P such that $\displaystyle \mathrm{AP}: \mathrm{AB}=2: 5$. Find the coordinates of P .
Point P(x, y) is equidistant from points A$\displaystyle (5, 1)$ and B$\displaystyle (1, 5)$. Prove that $\displaystyle \mathrm{x}=\mathrm{y}$.
Marking-scheme solution
\[\begin{aligned}
& \mathrm{AP}: \mathrm{AB}=2: 5 \Rightarrow \mathrm{AP}: \mathrm{PB}=2: 3 \\
& \mathrm{~A}(4,-5) \\
& \mathrm{x}=\frac{8+12}{5}=4, \mathrm{y}=\frac{10-15}{5}=-1 \\
& \text { Point } \mathrm{P} \text { is }(4,-1)
\end{aligned}
\]
\[\begin{aligned}
& \mathrm{PA}^{2}=\mathrm{PB}^{2} \Rightarrow(\mathrm{x}-5)^{2}+(\mathrm{y}-1)^{2}=(\mathrm{x}-1)^{2}+(\mathrm{y}-5)^{2} \\
& \Rightarrow \mathrm{x}=\mathrm{y}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.