Question

The area of the triangle formed by (-1, 2), (2, -1) and (0, 0) is

• A. 0
• B. 3
• C. 1
• D. \(\frac{3}{2}\)

Answer 1

The Correct Option is D

To find the area of a triangle formed by three points \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \), we use the formula: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] Substituting the points \( (-1, 2), (2, -1), (0, 0) \): \[ \text{Area} = \frac{1}{2} \left| (-1)(-1 - 0) + 2(0 - 2) + 0(2 + 1) \right| \] \[ = \frac{1}{2} \left| 1 - 4 + 0 \right| = \frac{1}{2} \times 3 = \frac{3}{2} \]

The correct option is (D): \(\frac{3}{2}\)