Class CBSE Class 12 Mathematics Matrices and Determinants Q #853
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
Let A be the area of a triangle having vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$. Which of the following is correct?
(A) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm A$
(B) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm2A$
(C) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm\frac{A}{2}$
(D) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|^{2}=A^{2}$
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Step-by-Step Solution

The area of a triangle with vertices $(x_1, y_1), (x_2, y_2)$, and $(x_3, y_3)$ is given by: $A = \frac{1}{2} |\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|$ Therefore, $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}| = \pm 2A$

Correct Answer: |\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm2A

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AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to recall and understand the formula for the area of a triangle using determinants.
Knowledge Dimension: FACTUAL
Justification: The question directly tests the student's knowledge of a specific formula (area of a triangle using determinants).
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question is based on direct recall of a formula from the textbook.

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