Answer:
16 units.
Explanation:
To find the perimeter of a polygon with vertices at (-2, 1), (-2, 4), (2, 7), (6, 4), and (6, 1), you can use the distance formula to calculate the distance between consecutive vertices and then sum those distances. The distance formula is:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's calculate the distances:
1. Between (-2, 1) and (-2, 4):
Distance = √[(-2 - (-2))^2 + (4 - 1)^2] = √(0 + 9) = √9 = 3
2. Between (-2, 4) and (2, 7):
Distance = √[(2 - (-2))^2 + (7 - 4)^2] = √(4^2 + 3^2) = √(16 + 9) = √25 = 5
3. Between (2, 7) and (6, 4):
Distance = √[(6 - 2)^2 + (4 - 7)^2] = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5
4. Between (6, 4) and (6, 1):
Distance = √[(6 - 6)^2 + (1 - 4)^2] = √(0 + (-3)^2) = √(0 + 9) = √9 = 3
Now, add up these distances to find the perimeter:
Perimeter = 3 + 5 + 5 + 3 = 16
So, the perimeter of the polygon is 16 units.