CUET · MATHS · PYQ PAPER 2025
If the points \(( a 1, b 1),( a 2, b 2)\) and \(( a 1+ a 2, b 1+ b 2)\) are collinear, then
- A \(a_1 b_1=-a_2 b_2\)
- B \(a_1 b_1=a_2 b_2\)
- C \(a_1 b_2=a_2 b_1\)
- D \(a_1 b_2=-a_2 b_1\)
Answer & Solution
Correct Answer
(C) \(a_1 b_2=a_2 b_1\)
Step-by-step Solution
Detailed explanation
\( \frac{b_2 - b_1}{a_2 - a_1} = \frac{(b_1+b_2) - b_2}{(a_1+a_2) - a_2} \) \( \frac{b_2 - b_1}{a_2 - a_1} = \frac{b_1}{a_1} \) \( a_1(b_2 - b_1) = b_1(a_2 - a_1) \) \( a_1 b_2 - a_1 b_1 = a_2 b_1 - a_1 b_1 \) \( a_1 b_2 = a_2 b_1 \)
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