Use Coordinate Geometry to Solve Problems Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. Find the perimeter of the polygon in kilometers. (1 point) Responses 104 square kilometers 104 square kilometers 46 square kilometers 46 square kilometers 46 kilometers 46 kilometers 34 square kilometers 34 square kilometers Skip to navigation
To find the perimeter of the polygon, we need to add up the lengths of all the sides.
Let's start by calculating the lengths of the three horizontal sides:
- Side AB: Coordinates of A are (-2,1) and B are (1,1)
Length = 1 - (-2) = 3 units
- Side BC: Coordinates of B are (1,1) and C are (3,3)
Length = √[(3-1)^2 + (3-1)^2] = √[2^2 + 2^2] = √(4+4) = √8 ≈ 2.83 units
- Side CD: Coordinates of C are (3,3) and D are (4,0)
Length = 3 - 0 = 3 units
Now, let's calculate the lengths of the two diagonal sides:
- Side AD: Coordinates of A are (-2,1) and D are (4,0)
Length = √[(-2-4)^2 + (1-0)^2] = √[(-6)^2 + 1^2] = √[36 + 1] = √37 ≈ 6.08 units
- Side BD: Coordinates of B are (1,1) and D are (4,0)
Length = √[(4-1)^2 + (0-1)^2] = √[3^2 + (-1)^2] = √[9 + 1] = √10 ≈ 3.16 units
The perimeter is therefore:
3 + 2.83 + 3 + 6.08 + 3.16 ≈ 17.07 units
Since each unit represents 1 kilometer, the perimeter of the polygon is 17.07 kilometers.
Therefore, the correct response is:
46 kilometers.