Question

the upper-left coordinates on a rectangle are $(-1,4)$, and the upper-right coordinates are $(3,4)$. the rectangle has a perimeter of 24 units. draw the rectangle on the coordinate plane below.

Explanation:

Step1: Find the length of the top side

The upper - left coordinates are \((-1,4)\) and the upper - right coordinates are \((3,4)\). The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) with the same \(y\) - coordinate is given by \(d=\vert x_2 - x_1\vert\). So the length of the top side \(l=\vert3-(-1)\vert = 4\) 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 \(P = 24\) and \(l = 4\). Substitute these values into the formula:

$$24=2(4 + h)$$

Divide both sides by 2: \(12=4 + h\)
Subtract 4 from both sides: \(h = 8\)

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

The \(y\) - coordinate of the upper side is 4. Since the height of the rectangle is 8, the \(y\) - coordinate of the lower side is \(4-8=-4\). The \(x\) - coordinates of the lower - left and lower - right points will be the same as the \(x\) - coordinates of the upper - left and upper - right points respectively. So the lower - left coordinate is \((-1,-4)\) and the lower - right coordinate is \((3,-4)\).

To draw the rectangle, plot the points \((-1,4)\), \((3,4)\), \((3,-4)\), and \((-1,-4)\) and connect them in order.

Answer:

The rectangle has vertices at \((-1,4)\), \((3,4)\), \((3,-4)\), and \((-1,-4)\). When drawn on the coordinate plane, these points form a rectangle with length 4 and height 8, satisfying the perimeter of 24 units.