Suppose a parallelogram is drawn on a coordinate plane. Using vertices with the coordinates (0,0)
, (2,3)
, (5,2)
, and (3,−1)
, compute the perimeter. Round your answer to the nearest tenth.(1 point)
The perimeter is approximately
units.
To find the perimeter of a parallelogram, we need to calculate the length of each side and then add them up.
Using the distance formula, we can calculate the length of each side:
Side 1: The distance between (0,0) and (2,3)
d1 = √((2-0)^2 + (3-0)^2) = √(2^2 + 3^2) = √(4 + 9) = √13
Side 2: The distance between (2,3) and (5,2)
d2 = √((5-2)^2 + (2-3)^2) = √(3^2 + (-1)^2) = √(9 + 1) = √10
Side 3: The distance between (5,2) and (3,-1)
d3 = √((3-5)^2 + (-1-2)^2) = √((-2)^2 + (-3)^2) = √(4 + 9) = √13
Side 4: The distance between (0,0) and (3,-1)
d4 = √((3-0)^2 + (-1-0)^2) = √(3^2 + (-1)^2) = √(9 + 1) = √10
Now we can add up the lengths of all sides to find the perimeter:
Perimeter = d1 + d2 + d3 + d4
Perimeter = √13 + √10 + √13 + √10
Using a calculator, we can find the numerical value of the approximate perimeter:
Perimeter ≈ 3.61 + 3.16 + 3.61 + 3.16 ≈ 13.54 units
Therefore, the perimeter of the parallelogram is approximately 13.54 units.