Question

an artist determines the location of a mural on a wall by mapping out the mural on a coordinate plane. The mural forms a triangle with vertices located at (-3, 5) , (-3, 7) and (4, 7) what is the area of the triangle in square units

Answer 1

The area of the triangle with vertices at (-3, 5), (-3, 7), and (4, 7) is calculated using the formula for the area of a triangle (1/2 × base × height), yielding 7 square units.

Step-by-step explanation:

The question involves calculating the area of a triangle on a coordinate plane with vertices at (-3, 5), (-3, 7), and (4, 7). To find the area of a triangle, you can use the formula: Area = 1/2 × base × height. In this case, the triangle's base and height can be easily determined from the coordinates given because the triangle's vertices form a right angle.

The base is the horizontal distance between the points (-3, 7) and (4, 7), which is 7 units (since both have the same y-coordinate). The height is the vertical distance between the points (-3, 5) and (-3, 7), which is 2 units (since both have the same x-coordinate).

Now, plug the base and height into the area formula:

Area = 1/2 × base × height
Area = 1/2 × 7 × 2
Area = 1/2 × 14
Area = 7 square units

Therefore, the area of the triangle is 7 square units.

Answer 2

The area of the triangle with vertices (-3, 5), (-3, 7), and (4, 7) is calculated using the base and height of the triangle and is found to be 7 square units.

Step-by-step explanation:

The student is asking for help to determine the area of a triangle with vertices located at (-3, 5), (-3, 7), and (4, 7) on a coordinate plane. We are dealing with a right triangle since two vertices have the same x-coordinate (-3), which means they are vertically aligned, creating a right angle at the vertex (-3, 5).

To find the area of the triangle, we need the base and the height. Here, the height is the difference in the y-coordinates of (-3, 5) and (-3, 7), which is 7 - 5 = 2 units. The base is the difference in the x-coordinates of (-3, 7) and (4, 7), which is 4 - (-3) = 7 units.

The formula for the area of a triangle is ½ × base × height. Therefore, the area of this triangle is ½ × 7 × 2 = 7 square units.