Question

Peeta draws a triangle on the coordinate grid. What is the area of their triangle in square units? a ( -7,3) b(5,8) c (0,-2)

(1 point)
Responses

120
120

47.5
47.5

65
65

40.5

Answer 1

To find the area of a triangle given its vertices on the coordinate grid, we can use the formula:

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

Where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are the coordinates of the vertices of the triangle.

Given the points:
- \( A(-7, 3) \) (let's say \( (x_1, y_1) = (-7, 3) \))
- \( B(5, 8) \) (let's say \( (x_2, y_2) = (5, 8) \))
- \( C(0, -2) \) (let's say \( (x_3, y_3) = (0, -2) \))

Now, we can substitute these coordinates into the formula:

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

Calculating each part:

1. \( 8 - (-2) = 8 + 2 = 10 \)
2. \( -2 - 3 = -5 \)

Now substituting back into the equation:

\[
\text{Area} = \frac{1}{2} \left| -7(10) + 5(-5) + 0 \right|
\]
\[
= \frac{1}{2} \left| -70 - 25 + 0 \right|
\]
\[
= \frac{1}{2} \left| -95 \right|
\]
\[
= \frac{1}{2} \times 95
\]
\[
= 47.5
\]

Thus, the area of the triangle is \( \boxed{47.5} \) square units.