Question

What is the area, in square units, of the triangle formed by the points \( (3, 2), (3, -6) \) and \( (5, 2) \)?

• A. 10
• B. 8
• C. 9
• D. 12

Hint:

To find the area of a triangle given its vertices, use the determinant-based formula for the area.

Answer 1

The Correct Option is B

The area of a triangle formed by the points \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) 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 \( (x_1, y_1) = (3, 2), (x_2, y_2) = (3, -6), (x_3, y_3) = (5, 2) \): \[ \text{Area} = \frac{1}{2} \left| 3((-6) - 2) + 3(2 - 2) + 5(2 - (-6)) \right| \] \[ = \frac{1}{2} \left| 3(-8) + 5(8) \right| = \frac{1}{2} \left| -24 + 40 \right| = \frac{1}{2} \times 16 = 8. \]