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. (1 point)
○ 14.1 units
○ 8 units
○ 22.8 units
○ 5.6 units

Explanation:

Step1: Calculate the distance between two points

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For points \((0,0)\) and \((4,4)\):
\(d_1=\sqrt{(4 - 0)^2+(4 - 0)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.7\)

Step2: Calculate another side length

For points \((4,4)\) and \((5,3)\):
\(d_2=\sqrt{(5 - 4)^2+(3 - 4)^2}=\sqrt{1+1}=\sqrt{2}\approx1.4\)

Step3: Calculate the perimeter

Perimeter of rectangle \(P = 2(d_1 + d_2)\)
\(P=2(\sqrt{32}+\sqrt{2})\approx2(5.7 + 1.4)=2\times7.1 = 14.2\approx14.1\) (due to rounding differences in intermediate steps)

Answer:

14.1 units