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 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.

Answer 1

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

Explanation:

You want to know a suitable strategy for finding the perimeter of a quadrilateral when the coordinates of its vertices are known.

Perimeter

The perimeter of a figure is the sum of its side lengths. When the coordinates of the ends of a side segment are known, the length of that segment can be found using the distance formula.

This should make it obvious that a suitable strategy for finding the perimeter is to find the length of each side and add the lengths.

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Additional comment

The slope is irrelevant when the perimeter is what you want.

The slope can be relevant if you're trying to prove a quadrilateral is a parallelogram or rectangle (or something else with parallel sides). (There are easier ways than using the slope.)

Multiplying side lengths will be relevant if you want the area of a rectangle. The product has no relation to the perimeter.

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