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

A=(-7,3)
B=(5,8)
C=0,-2)

Answer 1

To find the area of the triangle defined by the vertices \( A(-7, 3) \), \( B(5, 8) \), and \( C(0, -2) \), we can use the formula for the area of a triangle given by vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):

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

Substituting the coordinates of the points into the formula:

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

Now plug these values into the area formula:

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

Calculate each term:

1. Calculate \(8 - (-2) = 8 + 2 = 10\):
\[
(-7)(10) = -70
\]

2. Calculate \((-2) - 3 = -5\):
\[
5(-5) = -25
\]

3. For the third term, \(0(3 - 8) = 0\):
\[
0 = 0
\]

Now combine these results:
\[
-70 - 25 + 0 = -95
\]

Taking the absolute value:
\[
\left|-95\right| = 95
\]

Calculate the area:
\[
\text{Area} = \frac{1}{2}(95) = 47.5
\]

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