Question

you do: check for understanding
find the perimeter of the square in the coordinate plane below. round your answer to two decimal places
a. 11.31 units
b. 2.82 units
c. 7.95 units
d. 5.64 units

Explanation:

Step1: Assume side - length formula

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the length of one side of the square. Let's assume two adjacent vertices of the square have coordinates $(x_1,y_1)$ and $(x_2,y_2)$.

Step2: Calculate side - length

Suppose two adjacent vertices are $(0,0)$ and $(2,2)$. Then $d=\sqrt{(2 - 0)^2+(2 - 0)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.828$.

Step3: Calculate perimeter

The perimeter $P$ of a square is $P = 4s$, where $s$ is the side - length. So $P=4\times2\sqrt{2}=8\sqrt{2}\approx11.31$.

Answer:

A. 11.31 units