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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 5 · Set 2 · Q26
Using determinants, find the area of PQR with vertices P (3,1), Q (9,3) and R (5,7). Also, find the equation of line PQ using determinants.
Using determinants, find the area of $\displaystyle \triangle \mathrm{PQR}$ with vertices $\displaystyle \mathrm{P}(3,1), \mathrm{Q}(9,3)$ and $\displaystyle \mathrm{R}(5,7)$. Also, find the equation of line PQ using determinants.
Marking-scheme solution
Area $\displaystyle =\frac{1}{2}\left|\begin{array}{lll} 3 & 1 & 1 \\ 9 & 3 & 1 \\ 5 & 7 & 1 \end{array}\right|$
$$=\frac{1}{2}\{3(-4)-1(4)+1(48)\}=16 \text { sq. unit }
$$
Equation of PQ is $\displaystyle \left|\begin{array}{lll} \mathrm{x} & \mathrm{y} & 1 \\ 3 & 1 & 1 \\ 9 & 3 & 1 \end{array}\right|=0$
$\displaystyle -2 \mathrm{x}+6 \mathrm{y}=0 \quad$ or $\displaystyle \mathrm{x}-3 \mathrm{y}=0$
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CBSE Class 12 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.