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Graph and find the area of the figure with the vertices (−2, −2), (0, 0), (3, −2).

A. A=5 units^2
B.A=10 units^2
C. A= 4 units ^2
D. A=9 units ^2

User Einpoklum
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1 Answer

4 votes

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.

User Idontgetoutmuch
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