Final answer:
The perimeter of kite WXYZ can be found by using the distance formula on each pair of consecutive vertices and summing these distances, resulting in 2√(53) + 10 units for the correct perimeter.
Step-by-step explanation:
The student is asking about the perimeter of a kite with given vertices W(-3, 3), X(2, 3), Z(-3, -2), and Y(4, -4). To find the perimeter, we must calculate the distance between each pair of consecutive vertices (the kite's sides) and sum these distances.
The distance formula given two points (x1, y1) and (x2, y2) is √((x2-x1)² + (y2-y1)²). Applying this formula to the pairs of vertices:
- Side W to X: √((2-(-3))² + (3-3)²) = √(5²) = 5 units
- Side X to Y: √((4-2)² + (-4-3)²) = √(2² + (-7)²) = √(4 + 49) = √(53)
- Side Y to Z: √((-3-4)² + (-2-(-4))²) = √(-7² + 2²) = √(49 + 4) = √(53)
- Side Z to W: √((-3-(-3))² + (3-(-2))²) = √(0² + 5²) = 5 units
Since a kite has two pairs of adjacent sides equal in length, the two distances of √(53) are the same, and so are the two distances of 5 units. Therefore, the perimeter P is:
P = 2(√(53)) + 2(5) = 2√(53) + 10 units.
This matches option C, so the perimeter of kite WXYZ is 2√(53) + 10 units.