Question

Use a coordinate plane to create a rectangular park that has one corner at (−412, 312) and a perimeter of 30 units. Label the coordinates of each corner of the park. Then plot points with mixed number coordinates inside the park to represent a swing set, a slide, and a bench. Plot the slide farthest from the x-axis and the bench closest to the x-axis. What are the coordinates of the points you plotted?

Answer 1

A rectangle has four sides, where the opposite sides are equal

The possible coordinates are: (-4.5, 3.5), (-4.5,10.5), (3.5,3.5) and (3.5,10.5)

The coordinate point is given as:

$\mathbf{(x,y) = (-4\frac12,3\frac12)}$

Express as decimal

$\mathbf{(x,y) = (-4.5,3.5)}$

The perimeter is said to be 30 units.

So, we have:

$\mathbf{P = 2(L + W)}$

This gives

$\mathbf{2(L + W) = 30}$

Divide through by 2

$\mathbf{L + W = 15}$

This means that the sum of the dimensions is 15 units.

So, we can assume that:

Length =  8

Width = 7

So, the other coordinates are calculated as follows:

$\mathbf{(x,y) = (-4.5,3.5+7) = (-4.5,10.5)}$

$\mathbf{(x,y) = (-4.5 + 8,3.5) = (3.5,3.5)}$

$\mathbf{(x,y) = (-4.5+8,3.5+7) = (3.5,10.5)}$

So, the possible coordinates are: (-4.5, 3.5), (-4.5,10.5), (3.5,3.5) and (3.5,10.5)

See attachment for the graph of the rectangle

Read more about rectangles at:

https://brainly.com/question/22010143