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Use the image to answer the question.

A triangle is graphed by joining three plotted points on a coordinate plane. The x-axis ranges from negative 10 to 10 in increments of 2 and the y-axis ranges from negative 4 to 10 in increments of 2.

Peeta draws a triangle on the coordinate grid. What is the area of their triangle in square units?

(1 point)
Responses

120
120

40.5
40.5

65
65

47.5

1 answer

To determine the area of the triangle based on the coordinates provided, we'll need the coordinates of the triangle's vertices. Since the image is not visible to me, I'll outline the general method for calculating the area of a triangle given its vertices in a coordinate plane.

  1. Identify the coordinates of the vertices of the triangle: Let’s say the vertices are \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \).

  2. Use the area formula for a triangle with vertices on a coordinate plane: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

  3. Plug in the coordinates to calculate the area.

If you can provide the coordinates of the triangle or any additional details, I can help you calculate the area more specifically.

If the problem is multiple-choice and you do not need to perform the calculation, the areas given are: 120, 40.5, 65, and 47.5. Look for correlations in your triangle’s dimensions with these values if you can gauge visually, or use the area formula with the coordinates if you have them. If one of those options matches your calculation, that would be the answer.