Question

the vertices of a quadrilateral 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 side, and then determine if the opposite sides are parallel. use the slope formula to find the slope of each 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 perimeter concept

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

Step2: Analyze the options

• Using the distance formula to find the length of each side and then adding the lengths is the correct way to find the perimeter of a quadrilateral.
• Using the slope formula to find the slope of each side and then determining if the opposite sides are parallel is for checking the type of quadrilateral (like parallelogram) not for finding perimeter.
• Using the slope formula to find the slope of each side and then determining if the consecutive sides are perpendicular is for checking if it's a rectangle (if also parallelogram) or other right - angled figures, not for perimeter.
• Using the distance formula to find the length of the sides and then multiplying two of the side lengths is for finding the area of a rectangle (if it is a rectangle), not perimeter.

Answer:

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