Answer:
Explanation:
To find the area of the figure with the given vertices, we can use the formula for the area of a triangle. Since the three given points form a triangle, we can calculate its area.
Using the coordinates of the vertices, we have:
Vertex 1: (-2, -2)
Vertex 2: (0, 0)
Vertex 3: (3, -2)
The formula for the area of a triangle is:
A = (1/2) * base * height
To find the base and height of the triangle, we can use the distance formula between the given points.
Distance between Vertex 1 and Vertex 2:
base = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(0 - (-2))^2 + (0 - (-2))^2]
= √[2^2 + 2^2]
= √[4 + 4]
= √8
Distance between Vertex 2 and Vertex 3:
height = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(3 - 0)^2 + (-2 - 0)^2]
= √[3^2 + (-2)^2]
= √[9 + 4]
= √13
Now, we can calculate the area of the triangle:
A = (1/2) * base * height
= (1/2) * √8 * √13
= (1/2) * √104
= (1/2) * 2√26
= √26
Therefore, the area of the figure is √26 square units.
The correct option is not provided in the given answer choices.