B (5,8) A (-7,3) C (0 -2) Use the image to answer the question. Peeta draws a triangle on the coordinate grid. What is the area of their triangle in square units? (1 point)

1 answer

To calculate the area of a triangle given its vertices, you can use the following formula based on the coordinates of the vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):

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

Given the vertices of the triangle:

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

Let's assign the coordinates:

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

Plugging in the values:

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

Calculating each term:

  1. \( -7(8 + 2) = -7 \times 10 = -70 \)
  2. \( 5(-2 - 3) = 5 \times -5 = -25 \)
  3. \( 0(3 - 8) = 0 \)

Now substitute these into the formula:

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

This simplifies to:

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

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