Final answer:
The perimeter of the quadrilateral is found by calculating the distance between each pair of consecutive vertices and summing these distances. Using the distance formula, each side is determined to be 5 units long, resulting in a perimeter of 20 units (C).
Step-by-step explanation:
To find the perimeter of the quadrilateral with vertices at C (-2,1), D (2,4), E (5,0), and F (1,-3), we need to calculate the distance between each pair of consecutive vertices (CD, DE, EF, and FC) and then sum these distances. The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula √((x2 - x1)^2 + (y2 - y1)^2). By applying this formula to each pair of vertices, we can find the length of each side of the quadrilateral.
- Distance CD = √((2 - (-2))^2 + (4 - 1)^2) = √(16 + 9) = √25 = 5 units
- Distance DE = √((5 - 2)^2 + (0 - 4)^2) = √(9 + 16) = √25 = 5 units
- Distance EF = √((5 - 1)^2 + (0 - (-3))^2) = √(16 + 9) = √25 = 5 units
- Distance FC = √((-2 - 1)^2 + (1 - (-3))^2) = √(9 + 16) = √25 = 5 units
Adding up the lengths of all four sides, we get the perimeter of the quadrilateral: 5 + 5 + 5 + 5 = 20 units. Hence, the correct answer is C. 20 units.