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.
The perimeter is approximately units.
To find the perimeter of the parallelogram, we sum up the lengths of its four sides.
First, we find the length of the side connecting the points (0,0) and (2,3).
The distance between two points (x1, y1) and (x2, y2) is given by the formula: √((x2-x1)^2 + (y2-y1)^2).
Using this formula, we calculate the length of the first side:
√((2-0)^2 + (3-0)^2) = √(2^2 + 3^2) = √(4 + 9) = √13.
Next, we find the length of the side connecting the points (2,3) and (5,2):
√((5-2)^2 + (2-3)^2) = √(3^2 + (-1)^2) = √(9 + 1) = √10.
Then, we find the length of the side connecting the points (5,2) and (3,-1):
√((3-5)^2 + (-1-2)^2) = √((-2)^2 + (-3)^2) = √(4 + 9) = √13.
Finally, we find the length of the side connecting the points (3,-1) and (0,0):
√((0-3)^2 + (0-(-1))^2) = √((-3)^2 + (1)^2) = √(9 + 1) = √10.
Summing up the lengths of the four sides gives us:
√13 + √10 + √13 + √10 ≈ 6.3 + 6.3 ≈ 12.6.
Rounded to the nearest tenth, the perimeter is approximately 12.6 units.