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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 3 · Set 2 · Q28
(a) In what ratio does the X-axis divides the line segment joining the points(2, -3) and (5,6)? Also, find the coordinates of the point of…
(a)
In what ratio does the X-axis divides the line segment joining the points$\displaystyle (2, -3)$ and $\displaystyle (5,6)$ ? Also, find the coordinates of the point of intersection.
OR
(b)
Find the length of the median AD of $\displaystyle \triangle \mathrm{ABC}$ having vertices $\displaystyle \mathrm{A}(0,-1)$, B$\displaystyle (2, 1)$ and C$\displaystyle (0, 3)$.
Marking-scheme solution
Let the co ordinate of the point of intersection be ( \(\displaystyle \mathrm{x}, 0\) ).
Let ratio be k:$\displaystyle 1$
\[\begin{gathered}
\therefore \frac{6 \mathrm{k}-3}{\mathrm{k}+1}=0 \\
\Rightarrow \mathrm{k}=\frac{1}{2}
\end{gathered}
\]
∴ required ratio is $\displaystyle 1$: $\displaystyle 2$
\[\therefore x=\frac{5 \times 1+2 \times 2}{1+2}=\frac{9}{3}=3
\]
∴ the co ordinate of the point of intersection is \(\displaystyle (3,0)\)
Coordinate of D$\displaystyle (1,2)$.
\[\begin{aligned}
\mathrm{AD} & =\sqrt{(1-0)^{2}-(1+2)^{2}} \\
& =\sqrt{10}
\end{aligned}
\]
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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.