Question

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

Explanation:

Step1: Understand the concept of perimeter

Perimeter is the sum of the lengths of all sides of a figure.

Step2: Analyze each option

• Option A: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the length of each side (since in the coordinate plane, if we have two points \((x_1,y_1)\) and \((x_2,y_2)\) on a side of the figure, the distance between them is the length of that side). Then add the lengths. This is correct for finding the perimeter.
• Option B: Finding the slope of each side to check if opposite sides are parallel is used to determine if a figure is a parallelogram (a property of the figure, not its perimeter).
• Option C: Finding the slope of each side to check if consecutive sides are perpendicular is used to determine if a figure is a rectangle (a property of the figure, not its perimeter).
• Option D: Using the distance formula to find side - lengths and then multiplying two of them is used to find the area of a rectangle (not the perimeter).

Answer:

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