Final answer:
The perimeter of triangle ABC with given vertices is approximately 17.41, which is closest to the option C) 17.28.
Step-by-step explanation:
To find the perimeter of triangle ABC with vertices A(-2,1), B(-3,5), and C(3,6), we need to calculate the length of each side using the distance formula √((x2 - x1)² + (y2 - y1)²). The lengths of the sides are:
- AB: √((-3 + 2)² + (5 - 1)²) = √(17) ≈ 4.12
- BC: √((3 + 3)² + (6 - 5)²) = √(37) ≈ 6.08
- CA: √((3 + 2)² + (6 - 1)²) = √(52) ≈ 7.21
The perimeter P is the sum of these lengths: P = AB + BC + CA = 4.12 + 6.08 + 7.21 ≈ 17.41. Therefore, the closest answer from the options given is C) 17.28.