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 with y-axis (8, 6, 4, 2, -2, -4) and x-axis (-8, -6, -4, -2, 2, 4, 6, 8) grid, two blue dots at (-3,2) and (6,2) with blue lines down to (-3,-2) and (6,-2) (partially drawn rectangle)

Explanation:

Step1: Find the length of the top side

The upper - left coordinate is \((-3,2)\) and the upper - right coordinate is \((6,2)\). The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\) is given by \(d=\vert x_2 - x_1\vert\). So the length of the top side \(l=\vert6-(-3)\vert=\vert6 + 3\vert=9\) units.

Step2: Use the perimeter formula to find the height

The perimeter of a rectangle is given by \(P = 2(l + h)\), where \(l\) is the length and \(h\) is the height. We know that \(P = 30\) and \(l=9\). Substitute these values into the formula:

$$30=2(9 + h)$$

Divide both sides by 2:

$$15=9 + h$$

Subtract 9 from both sides:

$$h=15 - 9=6$$

units.

Step3: Determine the lower - left and lower - right coordinates

The upper - left coordinate is \((-3,2)\). To find the lower - left coordinate, we subtract the height from the \(y\) - coordinate of the upper - left coordinate. Since the height is 6, the \(y\) - coordinate of the lower - left coordinate is \(2-6=-4\). So the lower - left coordinate is \((-3,-4)\).
The upper - right coordinate is \((6,2)\). To find the lower - right coordinate, we subtract the height from the \(y\) - coordinate of the upper - right coordinate. The \(y\) - coordinate of the lower - right coordinate is \(2-6=-4\). So the lower - right coordinate is \((6,-4)\).

Step4: Draw the rectangle

Plot the points \((-3,2)\), \((6,2)\), \((6,-4)\) and \((-3,-4)\) on the coordinate plane and connect them to form the rectangle. The top side is between \((-3,2)\) and \((6,2)\), the right side is between \((6,2)\) and \((6,-4)\), the bottom side is between \((6,-4)\) and \((-3,-4)\), and the left side is between \((-3,-4)\) and \((-3,2)\).

Answer:

To draw the rectangle, plot the points \((-3,2)\), \((6,2)\), \((6,-4)\) and \((-3,-4)\) on the coordinate plane and connect them. The length of the rectangle is 9 units and the height is 6 units.