Question

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


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

Answer 1

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

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

Let’s assign the coordinates to the formula:

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

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. \( -7(8 + 2) = -7(10) = -70 \)
2. \( 5(-2 - 3) = 5(-5) = -25 \)
3. The third term, \( 0(3 - 8) = 0 \)

Now combine these:

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

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