A picture is shown of a triangle that is labeled ABC. The coordinates of each angle are A: (-7, 3), B: (5, 8), C: (0, -2).

Question

Peeta draws a triangle on the coordinate grid. What is the area of their triangle in square units? (1 point) Responses 65 65 47.5 47.5 120 120 40.5

Answer 1

To find the area of triangle ABC with vertices A(-7, 3), B(5, 8), and C(0, -2), we will use the formula for the area of a triangle given its vertex coordinates:

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

Assigning the coordinates:

• \( A(x_1, y_1) = (-7, 3) \)
• \( B(x_2, y_2) = (5, 8) \)
• \( C(x_3, y_3) = (0, -2) \)

Now substituting these coordinates into the formula:

\[ \text{Area} = \frac{1}{2} \left| -7(8 - (-2)) + 5((-2) - 3) + 0(3 - 8) \right| \]

Calculating each term:

1. \( 8 - (-2) = 8 + 2 = 10 \)

2. \( -7 \cdot 10 = -70 \)

3. \( -2 - 3 = -5 \)

4. \( 5 \cdot -5 = -25 \)

So, now substituting back into the area formula:

\[ \text{Area} = \frac{1}{2} \left| -70 - 25 + 0 \right| = \frac{1}{2} \left| -95 \right| = \frac{1}{2} \cdot 95 = 47.5 \]

Thus, the area of triangle ABC is \( 47.5 \) square units.

The correct answer is 47.5.