Question

the upper-left coordinates on a rectangle are $(-3, 2)$, and the upper-right coordinates are $(6, 2)$. the rectangle has a perimeter of 30 units.
draw the rectangle on the coordinate plane below.
coordinate plane image omitted

Explanation:

Step1: Calculate the length of the upper side

The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\vert x_2 - x_1\vert\) (since \(y_1 = y_2 = 2\)).
For the points \((-3,2)\) and \((6,2)\), the length \(l=\vert6-(-3)\vert=9\) units.

Step2: Use the perimeter formula to find the height

The perimeter formula of a rectangle is \(P = 2(l + w)\). Given \(P = 30\) and \(l=9\).
Substitute into the formula: \(30=2(9 + w)\).
First, divide both sides by 2: \(\frac{30}{2}=9 + w\), so \(15=9 + w\).
Then, subtract 9 from both sides: \(w=15 - 9 = 6\) units.
Since the upper - side is at \(y = 2\), the lower - side will be at \(y=2 - 6=-4\).
The lower - left coordinate is \((-3,-4)\) and the lower - right coordinate is \((6,-4)\).

Answer:

Plot the points \((-3,2)\), \((6,2)\), \((6,-4)\), \((-3,-4)\) and connect them to form the rectangle.