Final answer:
The perimeter of the quadrilateral with given coordinates is found by summing the distances between consecutive vertices, which for a rectangle is twice the sum of its width and height. In this case, the perimeter is 24 units.
Step-by-step explanation:
The question asks for the perimeter of a quadrilateral with given coordinates (-4,4), (2,4), (2,-2), and (-4,-2). To find the perimeter, we calculate the distances between consecutive points. The distance between two points is found using the distance formula √((x2-x1)² + (y2-y1)²).
The sides of this quadrilateral are horizontal and vertical lines, so the distances can be calculated by subtracting coordinates: The horizontal distance (width) is |2 - (-4)| = 6 units, and the vertical distance (height) is |4 - (-2)| = 6 units. Since opposite sides of a rectangle are equal, the perimeter P is the sum of all sides, which is 2 times the width plus 2 times the height. Therefore, P = 2 × width + 2 × height = 2 × 6 + 2 × 6 = 24 units.