Final answer:
The perimeter of the triangle with given vertices X(-6,1), Y(-6, 10), and Z(-2, 10) is calculated using the distance formula for each side and then summing up the distances to get a total of 22.85 units.
Step-by-step explanation:
To find the perimeter of a triangle with given coordinates, we first calculate the lengths of its sides using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by √((x2-x1)² + (y2-y1)²). Let’s apply this to the given coordinates X(-6,1), Y(-6, 10), and Z(-2, 10).
- The distance between X and Y is √((-6-(-6))² + (10-1)²) = √(0 + 81) = 9 units.
- The distance between Y and Z is √((-2-(-6))² + (10-10)²) = √(16 + 0) = 4 units.
- The distance between Z and X is √((-2-(-6))² + (10-1)²) = √(16 + 81) = √97 ≈ 9.85 units.
The perimeter is the sum of these side lengths: 9 + 4 + 9.85 = 22.85 units.