Final answer:
To find the perimeter of a regular pentagon, you need to calculate the length of one side using the distance formula. The distance between the endpoints (-1, 2) and (5, -6) is found to be 10 units. The perimeter of this regular pentagon is 50 units.
Step-by-step explanation:
To find the perimeter of a regular pentagon, you need to calculate the length of one side. Given that the endpoints of one side are (-1, 2) and (5, -6), you can use the distance formula to find the length of the side.
The distance formula is given by: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Using the coordinates (-1, 2) and (5, -6), we can calculate the length of the side as follows:
d = sqrt((5 - (-1))^2 + (-6 - 2)^2) = sqrt(6^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10 units.
The perimeter of a regular pentagon is equal to 5 times the length of one side, so the perimeter of this regular pentagon is 5 * 10 = 50 units.