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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 5 · Set 1 · Q24
Find the ratio in which the point $\displaystyle \mathrm{P}(-4,6)$ divides the line segment joining the points A$\displaystyle (-6,10)$ and B$\displaystyle (3, -8)$.Prove that the points $\displaystyle (3, 0)$, $\displaystyle (6, 4)$ and $\displaystyle (- 1, 3)$ are the vertices of an isosceles triangle.
Find the ratio in which the point $\displaystyle \mathrm{P}(-4,6)$ divides the line segment joining the points A$\displaystyle (-6,10)$ and B$\displaystyle (3, -8)$.
Prove that the points $\displaystyle (3, 0)$, $\displaystyle (6, 4)$ and $\displaystyle (- 1, 3)$ are the vertices of an isosceles triangle.
Marking-scheme solution
Let the ratio be k:$\displaystyle 1$
\[\begin{aligned}
& -4=\frac{3 k-6}{k+1} \\
& \Rightarrow k=\frac{2}{7}
\end{aligned}
\]
Let A$\displaystyle (3,0)$, B$\displaystyle (6,4)$, C$\displaystyle (-1, 3)$
\[\begin{aligned}
& \mathrm{AB}=\sqrt{(3-6)^{2}+(0-4)^{2}}=5 \\
& \mathrm{BC}=\sqrt{(6+1)^{2}+(4-3)^{2}}=\sqrt{50} \\
& \mathrm{CA}=\sqrt{(3+1)^{2}+(0-3)^{2}}=5 \\
& \quad \mathrm{As}, \mathrm{AB}=\mathrm{AC} \\
& \Rightarrow \mathrm{ABC} \text { is an isosceles triangle }
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.