CUET · MATHS · PYQ PAPER 2023
If three points \(A \left(a_1, b_1\right), B \left(a_2, b_2\right)\) and \(C \left(a_3, b_3\right)\) are collinear and D is the determinant of their coordinates with a column of 1s, then:
- A D = 0
- B D = \pm 1
- C \(D ^2=0\) or 1
- D \(D =\left(a_1+a_2+a_3\right)-\left(b_1+b_2+b_3\right)\)
Answer & Solution
Correct Answer
(A) D = 0
Step-by-step Solution
Detailed explanation
If three points are collinear, the area of the triangle formed by them is 0. The determinant \(D = \begin{vmatrix} a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ a_3 & b_3 & 1 \end{vmatrix}\) represents twice the area of the triangle. Therefore, \(D = 0\).
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