Question

Area of the triangle formed by the points \((-5, -1)\), \((3, -5)\) and \((5, 2)\) is:

• A. 32
• B. 22
• C. 42
• D. 52

Hint:

To find the area of a triangle given three vertices, use the formula: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

Answer 1

The Correct Option is B

The area of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is given by the formula: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] Substituting the coordinates \((-5, -1)\), \((3, -5)\), and \((5, 2)\): \[ \text{Area} = \frac{1}{2} \left| (-5)(-5 - 2) + 3(2 + 1) + 5(-1 + 5) \right| \] \[ \text{Area} = \frac{1}{2} \left| (-5)(-7) + 3(3) + 5(4) \right| \] \[ \text{Area} = \frac{1}{2} \left| 35 + 9 + 20 \right| = \frac{1}{2} \times 64 = 32 \] Thus, the correct answer is option (2).