Final answer:
To find the perimeter of the polygon, calculate the distance between each pair of consecutive vertices and add up these distances. The perimeter of the polygon is approximately 15.3 units.
Step-by-step explanation:
To find the perimeter of a polygon, you need to calculate the distance between each pair of consecutive vertices and then add up these distances.
Let's calculate the distance between (-2,-2) and (3,-3):
Distance = sqrt[(3 - (-2))^2 + (-3 - (-2))^2] = sqrt[5^2 + 1^2] = sqrt[25 + 1] = sqrt[26]
Similarly, the distances between consecutive vertices are:
Between (3,-3) and (4,-6): sqrt[(4 - 3)^2 + (-6 - (-3))^2] = sqrt[1^2 + 3^2] = sqrt[1 + 9] = sqrt[10]
Between (4,-6) and (-2,-4): sqrt[(-2 - 4)^2 + (-4 - (-6))^2] = sqrt[(-6)^2 + 2^2] = sqrt[36 + 4] = sqrt[40]
Between (-2,-4) and (-2,-2): sqrt[(-2 - (-2))^2 + (-2 - (-4))^2] = sqrt[0^2 + 2^2] = sqrt[0 + 4] = sqrt[4]
To find the perimeter, add up these distances: sqrt[26] + sqrt[10] + sqrt[40] + sqrt[4] = approximately 15.3 units.
Therefore, the correct answer is A) 15.3 units.