Question

The area of the triangle with vertices \( (1, 1), (-4, 6), (-3, -5) \) is?

• A. 20
• B. 24
• C. 30
• D. 35

Hint:

Use the area formula for a triangle with given vertices to calculate the area.

Answer 1

The Correct Option is B

Step 1: Using the formula for the area of a triangle with given vertices.
The area \( A \) of a triangle with vertices \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) is given by: \[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] Step 2: Substitute the coordinates of the vertices.
We are given the points:
\( (x_1, y_1) = (1, 1) \)
\( (x_2, y_2) = (-4, 6) \)
\( (x_3, y_3) = (-3, -5) \)
Substitute into the area formula: \[ A = \frac{1}{2} \left| 1(6 + 5) + (-4)(-5 - 1) + (-3)(1 - 6) \right| \] Simplifying the expression: \[ A = \frac{1}{2} \left| 1 \times 11 + (-4) \times (-6) + (-3) \times (-5) \right| \] \[ A = \frac{1}{2} \left| 11 + 24 + 15 \right| = \frac{1}{2} \times 50 = 24 \]