Final answer:
To find the exact perimeter of quadrilateral ABCD, calculate the distance between each pair of consecutive points using the distance formula and add these distances together.
Step-by-step explanation:
To find the exact perimeter of quadrilateral ABCD, we need to calculate the distance between each pair of consecutive points and then add these distances up.
The distance between two points (x1, y1) and (x2, y2) in the
Cartesian plane is given by the formula d = {(x2 - x1)^2 + (y2 - y1)^2}^1/2.
First, calculate the distances of each side:
- AB: d = {(6 - (-3))^2 + ((-2) - 2)^2}^1/2 = {81 + 16}^1/2 ={97}^1/2
- BC: d = {(3 - 6)^2 + ((-6) - (-2))^2}^1/2 = {9 + 16}^1/2 = {25}^1/2 = 5
- CD: d = {(3 - 0)^2 + ((-6) - (-6))^2}^1/2 = {9 + 0}^1/2 = {9}^1/2 = 3
- AD: d = {((-3) - 0)^2 + (2 - (-6))^2}^1/2 = \sqrt{9 + 64}^1/2 = {73}^1/2
Finally, add the lengths of all four sides to get the perimeter:
Perimeter of ABCD = AB + BC + CD + AD = sqrt{97}^1/2 + 5 + 3 + \{73}^1/2