CUET · MATHS · PYQ PAPER 2023
If \(K\) is such that the area of triangle \(A B C\) is 3 , where \(A(1,3), B(0,0)\) and \(C(K, 0)\), then the value(s) of \(K\) is/are:
- A 0
- B \(\pm 1\)
- C \(\pm 2\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(C) \(\pm 2\)
Step-by-step Solution
Detailed explanation
Area \( = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| \) \( 3 = \frac{1}{2} |1(0 - 0) + 0(0 - 3) + K(3 - 0)| \) \( 3 = \frac{1}{2} |3K| \) \( 6 = |3K| \) \( 3K = \pm 6 \) \( K = \pm 2 \)
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