CUET · MATHS · PYQ PAPER 2025
If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where k > 0 is 30 sq. units, then the value of k is
- A 4
- B 27
- C \(\frac{4}{27}\)
- D \(\frac{27}{4}\)
Answer & Solution
Correct Answer
(B) 27
Step-by-step Solution
Detailed explanation
\(30 = \frac{1}{2} |(-1)(-5 - 2) + (1)(2 - 3) + (k)(3 - (-5))|\) \(60 = |-1(-7) + 1(-1) + k(8)|\) \(60 = |7 - 1 + 8k|\) \(60 = |6 + 8k|\) \(60 = 6 + 8k \quad (\text{since } k > 0)\) \(54 = 8k\) \(k = \frac{54}{8} = \frac{27}{4}\)
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