Question

the upper-left coordinates on a rectangle are (3, -3), and the upper-right coordinates are (7, -3). the rectangle has an area of 16 square units. draw the rectangle on the coordinate plane below.

Explanation:

Step1: Find the length of the top side

The upper - left coordinate is \((3,-3)\) and the upper - right coordinate is \((7,-3)\). The distance between two points with the same \(y\) - coordinate \((x_1,y)\) and \((x_2,y)\) is given by \(d=\vert x_2 - x_1\vert\). So the length of the top side \(l=\vert7 - 3\vert=4\) units.

Step2: Find the height of the rectangle

The area of a rectangle is given by \(A = l\times h\), where \(A = 16\) square units and \(l = 4\) units. We can solve for the height \(h\) using the formula \(h=\frac{A}{l}\). Substituting the values, we get \(h=\frac{16}{4}=4\) units.

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

Since the rectangle is vertical, the \(x\) - coordinates of the lower - left and lower - right points will be the same as the upper - left and upper - right points respectively. The \(y\) - coordinate of the lower points will be \(y=-3 - 4=-7\) (because we move down 4 units from \(y = - 3\)). So the lower - left coordinate is \((3,-7)\) and the lower - right coordinate is \((7,-7)\).

To draw the rectangle, we plot the points \((3,-3)\), \((7,-3)\), \((7,-7)\), and \((3,-7)\) and connect them in order.

Answer:

The rectangle has vertices at \((3,-3)\), \((7,-3)\), \((7,-7)\), and \((3,-7)\). When drawing on the coordinate plane, plot these four points and connect them to form the rectangle.