Question

What is the area of the triangle?
Point A: (-3, -3)
Point B: (-2, 4)
Point C: (6, 5)

A. 30 square units
B. 44 square units
C. 27.5 square units

Answer 1

To find the area of the triangle formed by points A, B, and C, we can use the formula for the area of a triangle given by the coordinates of its vertices:

\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

In our case, the coordinates of the points are:
- Point A: \( (x_1, y_1) = (-3, -3) \)
- Point B: \( (x_2, y_2) = (-2, 4) \)
- Point C: \( (x_3, y_3) = (6, 5) \)

Now we substitute these coordinates into the formula:

\[
\text{Area} = \frac{1}{2} \left| -3(4 - 5) + (-2)(5 - (-3)) + 6((-3) - 4) \right|
\]

Calculating each term step-by-step:

1. For the first term: \( -3(4 - 5) = -3(-1) = 3 \)
2. For the second term: \( -2(5 - (-3)) = -2(5 + 3) = -2(8) = -16 \)
3. For the third term: \( 6((-3) - 4) = 6(-7) = -42 \)

Now, we combine these results:

\[
\text{Area} = \frac{1}{2} \left| 3 - 16 - 42 \right|
\]
\[
= \frac{1}{2} \left| 3 - 16 - 42 \right| = \frac{1}{2} \left| 3 - 58 \right| = \frac{1}{2} \left| -55 \right| = \frac{1}{2} \times 55 = 27.5
\]

Thus, the area of the triangle is:

\[
\text{Area} = 27.5 \text{ square units}
\]

The correct answer is **C. 27.5 square units**.