Question

Find the base and height of a rectangle with vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1). The height is units. The base is units.

Answer 1

The height is 6 units.

The base is 2 units.

EXPLANATION

The given rectangle has vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1).

To find the height of the rectangle, we use the points (-2,7) and (-2,1) or

(-4,7) and (-4,1) because they form the vertical side of the rectangle.

The height is

`|7-1|=6 units`

To find the base, use the points (-2,7) and (-4,7) or (-2,1) and (-4,1).

The base is

`|-2--4|=2 units`

Answer 2

Answer: The base is 2 units and the height is 6 units.

Explanation:

You can plot the points (-4, 7), (-2, 7), (-2, 1), and (-4, 1) and obtain the rectangle shown in the figure attached.

As you can see in the figure, the distance between the points of the base is:

`d=√((-2-(-4))^2+(1-1)^2)\\d=2`

Then the lenght of the base is 2 units

The distance between the points of the height is:

`d=√((-2-(-2))^2+(1-7)^2)\\d=6`

Then the height is 6 units