calculator\nwhat is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a…

Explanation:

Step1: Find the length of one side using the distance formula

The distance formula is (d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}). Let's assume two adjacent vertices of the rectangle. For example, if we take two points ((-7, - 1)) and ((-5,4)) [ \begin{align*} d_1&=\sqrt{(-5+7)^2+(4 + 1)^2}\ &=\sqrt{(2)^2+(5)^2}\ &=\sqrt{4 + 25}\ &=\sqrt{29}\approx5.4 \end{align*} ]

Step2: Find the length of the other side using the distance formula

Take another two adjacent vertices, say ((-5,4)) and ((3,2)) [ \begin{align*} d_2&=\sqrt{(3 + 5)^2+(2-4)^2}\ &=\sqrt{(8)^2+(-2)^2}\ &=\sqrt{64+4}\ &=\sqrt{68}\approx8.2 \end{align*} ]

Step3: Calculate the perimeter of the rectangle

The perimeter formula of a rectangle is (P=2(l + w)). Here (l\approx8.2) and (w\approx5.4) [ \begin{align*} P&=2(8.2+5.4)\ &=2\times13.6\ & = 30.6 \end{align*} ]

Answer:

30.6 units