Question

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.

Answer 1

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.