KCET2026MathematicsStraight Lines
The area of the triangle with vertices (3, 8), (-4, 2) and (5, 1) is P 4 , then the value of P is
Options
- A61 2
- B2 61
- C122
- D1 122
Correct answer
C. 122
Step-by-step solution
The area of a triangle with vertices (x₁, y₁) , (x₂, y₂) , and (x₃, y₃) is given by 1 2 |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)| . Substituting the given vertices (3, 8) , (-4, 2) , and (5, 1) : Area = 1 2 |3(2 - 1) - 4(1 - 8) + 5(8 - 2)| Area = 1 2 |3(1) - 4(-7) + 5(6)| Area = 1 2 |3 + 28 + 30| = 61 2 Given that the area is P 4 : P 4 = 61 2 P = 122 Answer: 122