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.

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. 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 \((x_2,y_2)\) (which gives the length of a side of the quadrilateral). Slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) is for finding the slope of a line (related to parallel or perpendicular lines, not perimeter). Multiplying side lengths is for area (e.g., in rectangles \(A = l\times w\)), not perimeter.

Answer:

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