Final answer:
The perimeter of the triangle with vertices at (3,2), (3,-3), and (-2,-3) is calculated by finding the lengths of the three sides using the distance formula and adding them together, resulting in 17.07 units (rounded to the nearest hundredth) which does not match the given options.
Step-by-step explanation:
The question is seeking the perimeter of a triangle with given vertices. To find this, we calculate the distance between each pair of points and add them up. The distances between the points are found using the distance formula. For points (x1, y1) and (x2, y2), it is √((x2 - x1)² + (y2 - y1)²).
Here are the sides of the triangle and their lengths:
- Side 1, between (3,2) and (3,-3): √((3 - 3)² + (-3 - 2)²) = 5 units
- Side 2, between (3,-3) and (-2,-3): √((-2 - 3)² + (-3 - (-3))²) = 5 units
- Side 3, between (-2,-3) and (3,2): √((3 - (-2))² + (2 - (-3))²) = √(5² + 5²) = √50 ≈ 7.07 units
The perimeter is the sum of these lengths: 5 units + 5 units + 7.07 units = 17.07 units. Rounding to the nearest hundredth gives us 17.07 units, but this does not match any of the provided options (a-d). It seems there might be an error in the question or the given options.