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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 3 · Set 1 · Q29
(a) Find the ratio in which the line segment joining the points (5,3) and (-1, 6) is divided by Y-axis.
(a)
Find the ratio in which the line segment joining the points $\displaystyle (5,3)$ and $\displaystyle (-1, 6)$ is divided by Y-axis.
OR
(b)
$\displaystyle \mathrm{P}(-2,5)$ and $\displaystyle \mathrm{Q}(3,2)$ are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR.
Marking-scheme solution
(a)
Let the line segment divides y-axis at ($\displaystyle 0$, y).
Let the required ratio be k : $\displaystyle 1$
\[\begin{aligned}
\therefore \quad & 0=\frac{(-1) \mathrm{k}+5(1)}{\mathrm{k}+1} \\
\Rightarrow \quad & \mathrm{k}=5
\end{aligned}
\]
Hence ratio is $\displaystyle 5$ : $\displaystyle 1$
OR
(b)
Let coordinates of R be (x, y) .
\[\begin{aligned}
& P R: R Q=2: 1 \\
& x=\frac{2(3)+1(-2)}{2+1}=\frac{4}{3} \\
& y=\frac{2(2)+1(5)}{2+1}=3
\end{aligned}
\]
∴ Cordinates of the point \(\displaystyle \mathrm{R}\left(\frac{4}{3}, 3\right)\)
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.