Suppose a parallelogram is drawn on a coordinate plane. Using vertices with the coordinates (2,1)
, (2,3)
, (4,4)
, and (4,2)
, compute the perimeter. Round your answer to the nearest tenth.
To compute the perimeter of a parallelogram, we need to calculate the length of all four sides and add them together.
Let's label the points as follows:
A(2,1) is the bottom left corner.
B(2,3) is the top left corner.
C(4,4) is the top right corner.
D(4,2) is the bottom right corner.
To find the length of side AB, we calculate the distance between points A and B using the distance formula:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((2 - 2)^2 + (3 - 1)^2)
= sqrt(0^2 + 2^2)
= sqrt(0 + 4)
= sqrt(4)
= 2
Similarly, the length of side BC can be calculated as:
BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 2)^2 + (4 - 3)^2)
= sqrt(2^2 + 1^2)
= sqrt(4 + 1)
= sqrt(5)
≈ 2.236
The length of side CD can be found using the same method:
CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 4)^2 + (2 - 4)^2)
= sqrt(0^2 + (-2)^2)
= sqrt(0 + 4)
= sqrt(4)
= 2
Finally, we compute the length of side AD:
AD = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 2)^2 + (2 - 1)^2)
= sqrt(2^2 + 1^2)
= sqrt(4 + 1)
= sqrt(5)
≈ 2.236
Now, we can add up the lengths of all four sides to find the perimeter:
Perimeter = AB + BC + CD + AD
= 2 + 2.236 + 2 + 2.236
≈ 8.472
Rounding to the nearest tenth, the perimeter of the parallelogram is approximately 8.5.