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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 4 · Set 1 · Q36
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day.…
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions :
(ii)
(a)
What is the distance between the points A and C ?
OR
(b)
Find the coordinates of the point which divides the line segment joining the points A and B in the ratio $\displaystyle 1: 3$ internally.
(iii)
What are the coordinates of the point D ?
Marking-scheme solution
(i)
Mid point of FG is $\displaystyle \left(\frac{-3+1}{2}, \frac{0+4}{2}\right)=(-1,2)$
(ii)
(a)
\[\begin{aligned}
\mathrm{AC} & =\sqrt{(-1-3)^{2}+(-2-4)^{2}} \\
& =\sqrt{52} \text { or } 2 \sqrt{13}
\end{aligned}
\]
OR
(b)
The coordinates of required point are $\displaystyle \left(\frac{1 \times 3+3 \times 3}{1+3}, \frac{1 \times 2+3 \times 4}{1+3}\right)$
i.e. $\displaystyle \left(3, \frac{7}{2}\right)$
(iii)
D$\displaystyle (-2, -5)$
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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.