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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 2 · Set 1 · Q23
Show that the points (-2, 3), (8,3) and (6,7) are the vertices of a right-angled triangle.
Show that the points $\displaystyle (-2, 3)$, $\displaystyle (8,3)$ and $\displaystyle (6,7)$ are the vertices of a right-angled triangle.
Marking-scheme solution
Let the given points be A $\displaystyle (-2, 3)$, B $\displaystyle (8, 3)$ and C $\displaystyle (6, 7)$
Then, \(\displaystyle \mathrm{AB}=10, \mathrm{BC}=\sqrt{4+16}=\sqrt{20}\),
\[\mathrm{AC}=\sqrt{64+16}=\sqrt{80}
\]
\(\displaystyle \therefore \mathrm{AB}^{2}=\mathrm{BC}^{2}+\mathrm{AC}^{2}\)
∴ the given points are the vertices of a right angled triangle.
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.