Final answer:
The perimeter of the triangle with vertices A(-2,2), B(10,2), and C(10,7) is 30 units, calculated using the distance formula for each pair of vertices.
Step-by-step explanation:
To find the perimeter of the triangle with vertices A(-2,2), B(10,2), C(10,7), we first calculate the lengths of the sides using the distance formula. Since points A and B lie on the same horizontal line (y-coordinate is the same), the distance between A and B is simply the difference in their x-coordinates, which is 10 - (-2) = 12 units. Similarly, since points B and C share the same vertical line (x-coordinate is the same), the distance between B and C is the difference in their y-coordinates, which is 7 - 2 = 5 units. To find the length of the side AC, we use the distance formula: √((x2 - x1)² + (y2 - y1)²), which gives us √((10 - (-2))² + (7 - 2)²) = √(144 + 25) = √169 = 13 units. Thus, the perimeter of the triangle is the sum of the lengths of its sides, which is 12 + 5 + 13 = 30 units.