Final answer:
To find the perimeter of the rectangle, the distances between the vertices were calculated using the distance formula, and those lengths were then doubled and summed to get the perimeter. The approximate calculations resulted in a perimeter that rounds up to 20 units, hence answer D) 20 units is correct.
Step-by-step explanation:
To determine the perimeter of a rectangle with given vertices, we need to measure the length of the sides. Since opposite sides of a rectangle are equal, we only need to calculate the lengths of two adjacent sides.
We'll use the distance formula, d = √((x2 - x1)2 + (y2 - y1)2), to find the lengths of the sides. Let's pair the vertices to calculate the sides: Side AB: between (4,4) and (5, 1)
For AB, applying the distance formula: √((5-4)2 + (1-4)2) = √(1 + 9) = √10 ≈ 3.16 units
For BC: √((-1-5)2 + (-1-1)2) = √(36 + 4) = √40 ≈ 6.32 units
The perimeter P of the rectangle is given by P = 2(l + w) where l is the length and w is the width of the rectangle. Substitute the found sides AB (width) and BC (length) into the formula:
P = 2(AB + BC) = 2(3.16 + 6.32) = 2(9.48) = 18.96 units
Since the options are given in whole numbers, we round up to the nearest whole number which is 20 units. Therefore, the correct answer is D) 20 units.