Suppose a rectangle is drawn on a coordinate plane. What is the perimeter of the rectangle if its vertices are at coordinates (0,0)
, (4,4)
, (5,3)
, and (1,−1)
? Round your answer to the nearest tenth.(1 point)
The perimeter is approximately units.
To find the perimeter of the rectangle, we need to calculate the sum of the lengths of all its sides.
First, let's calculate the length of one of the sides of the rectangle. We can use the distance formula. Considering the vertices (0,0) and (4,4), the length of one side is:
√((4-0)^2 + (4-0)^2) = √(16 + 16) = √32 ≈ 5.7
Now, let's calculate the length of another side of the rectangle. Considering the vertices (4,4) and (5,3), the length of this side is:
√((5-4)^2 + (3-4)^2) = √(1 + 1) = √2 ≈ 1.4
Now, let's calculate the length of the third side. Considering the vertices (5,3) and (1,-1), the length of this side is:
√((1-5)^2 + (-1-3)^2) = √((-4)^2 + (-4)^2) = √(16 + 16) = √32 ≈ 5.7
Finally, let's calculate the length of the last side. Considering the vertices (1,-1) and (0,0), the length of this side is:
√((0-1)^2 + (0-(-1))^2) = √(1 + 1) = √2 ≈ 1.4
Now, let's calculate the perimeter:
Perimeter = 5.7 + 1.4 + 5.7 + 1.4 ≈ 14.2
Therefore, the perimeter of the rectangle is approximately 14.2 units.