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 a rectangle, we need to sum the lengths of all four sides.
The distance between (0,0) and (4,4) can be found using the distance formula:
d = sqrt((4-0)^2 + (4-0)^2) = sqrt(4^2 + 4^2) = sqrt(16 + 16) = sqrt(32) = 4sqrt(2)
The distance between (4,4) and (5,3) can be found using the distance formula:
d = sqrt((5-4)^2 + (3-4)^2) = sqrt(1^2 + (-1)^2) = sqrt(1 + 1) = sqrt(2)
The distance between (5,3) and (1,-1) can be found using the distance formula:
d = sqrt((1-5)^2 + (-1-3)^2) = sqrt((-4)^2 + (-4)^2) = sqrt(16 + 16) = sqrt(32) = 4sqrt(2)
The distance between (1,-1) and (0,0) can be found using the distance formula:
d = sqrt((0-1)^2 + (0-(-1))^2) = sqrt((-1)^2 + 1^2) = sqrt(1 + 1) = sqrt(2)
Now we can sum all four sides:
4sqrt(2) + sqrt(2) + 4sqrt(2) + sqrt(2) = 10sqrt(2)
To round the answer to the nearest tenth, we get:
10sqrt(2) ≈ 14.1 units