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.
To find the perimeter of the rectangle, we need to find the lengths of its four sides and add them up.
Using the distance formula, the lengths of the sides are:
Side 1: Distance between (0,0) and (4,4)
d₁ = sqrt((4-0)² + (4-0)²) = sqrt(16 + 16) = sqrt(32) ≈ 5.7
Side 2: Distance between (4,4) and (5,3)
d₂ = sqrt((5-4)² + (3-4)²) = sqrt(1 + 1) = sqrt(2) ≈ 1.4
Side 3: Distance between (5,3) and (1,-1)
d₃ = sqrt((1-5)² + (-1-3)²) = sqrt(16 + 16) = sqrt(32) ≈ 5.7
Side 4: Distance between (1,-1) and (0,0)
d₄ = sqrt((0-1)² + (0-(-1))²) = sqrt(1 + 1) = sqrt(2) ≈ 1.4
Therefore, the perimeter of the rectangle is approximately 5.7 + 1.4 + 5.7 + 1.4 = 14.2.