Final answer:
The perimeter of the triangle is found by calculating the lengths of its sides using the distance formula and summing these lengths. The perimeter is 24 units.
Step-by-step explanation:
The question involves calculating the perimeter of a triangle with given vertices. We're provided with three vertices that define the triangle: (-9, 2), (-9, -6), and (-3, -6). To find the perimeter, we need to determine the lengths of the sides by using the distance formula between two points, which is √((x2-x1)² + (y2-y1)²).
Let's calculate each side:
- Side 1 (between (-9, 2) and (-9, -6)): Length is the difference in the y-coordinates, which is |2 - (-6)| = 8 units.
- Side 2 (between (-9, -6) and (-3, -6)): Length is the difference in the x-coordinates, which is |-3 - (-9)| = 6 units.
- Side 3 (between (-3, -6) and (-9, 2)): Use the distance formula to find the length, which is √((-9 - (-3))² + (2 - (-6))²) = √(6² + 8²) = √(36 + 64) = √100 = 10 units.
The perimeter of the triangle is the sum of these lengths: 8 units + 6 units + 10 units = 24 units.