Use the image to answer the question.

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

47.5
47.5

65
65

Answer 1

To determine the area of the triangle, you can use the formula for the area of a triangle given the coordinates of its vertices:

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

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

Given that I don't have the visual reference to Peeta's triangle, I'm unable to provide the exact vertices or confirm the area directly just from the options without the coordinates.

However, if you know the coordinates of the vertices of the triangle, you can substitute them into the formula to compute the area.

Please provide the coordinates of the triangle's vertices, and I will help you calculate the area! If the problem is meant to be a multiple-choice question based on those answer choices, then I suggest checking the calculations to see which one fits based on the coordinates you can find.