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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 2 · Set 1 · Q22
Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5).
Find the type of triangle ABC formed whose vertices are A$\displaystyle (1, 0)$, B$\displaystyle (-5, 0)$ and C$\displaystyle (-2, 5)$.
Marking-scheme solution
\[\begin{aligned}
& A(1,0) \quad B(-5,0) \quad C(-2,5) \\
& A B=\sqrt{(-5-1)^{2}+(0-0)^{2}}=6 \\
& B C=\sqrt{(-5+2)^{2}+(0-5)^{2}}=\sqrt{34} \\
& C A=\sqrt{(1+2)^{2}+(0-5)^{2}}=\sqrt{34} \\
& \therefore B C=C A \\
& \text { So, } \triangle A B C \text { is isosceles. }
\end{aligned}
\]
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