Question

the vertices of a quadrilateral in the coordinate - plane are known. how can the perimeter of the figure be found? use the slope formula to find the slope of each side, and then determine if the consecutive sides are perpendicular. use the slope formula to find the slope of each side, and then determine if the opposite sides are parallel. use the distance formula to find the length of the sides, and then multiply two of the side lengths. use the distance formula to find the length of each side, and then add the lengths.

Explanation:

Step1: Recall perimeter concept

Perimeter is the sum of side - lengths.

Step2: Analyze methods for side - length calculation

To find the perimeter of a quadrilateral in the coordinate plane, we need to find the length of each side. The distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ is used to find the length between two points $(x_1,y_1)$ and $(x_2,y_2)$. After finding the length of each side, we add them together.

Answer:

Use the distance formula to find the length of each side, and then add the lengths.