Final answer:
The perimeter of the polygon formed by points A(-6,6), B(9,6), and C(9,-2) is calculated using the distance formula and the definitions of horizontal and vertical distances, resulting in a total of 40 units.
Step-by-step explanation:
The perimeter of the polygon formed by connecting the points A(-6,6), B(9,6), and C(9,-2) can be calculated by finding the length of each side and then summing these lengths. Using the distance formula, √((x2-x1)² + (y2-y1)²), we can calculate the distances AB, BC, and AC (which will be the same as CA since we have to return to the starting point A to complete the polygon). AB is the distance between points A and B, BC is between points B and C, and AC is the straight line back to the starting point A from C.
The length of AB (horizontal line) is straightforward since the y-coordinates are the same, so AB = 9 - (-6) = 15 units. The length of BC (vertical line) is also a direct calculation since the x-coordinates are the same, so BC = 6 - (-2) = 8 units. Finally, AC is the length of the hypotenuse of the right-angled triangle formed by AB and BC, so AC = √(15² + 8²) = √(225 + 64) = 17 units. Adding these gives us the perimeter of the polygon: 15 + 8 + 17 = 40 units.