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)
the perimeter is approximately units
14.0
14.1
13.1
12.6

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 \((4,4)\):
\(d_1=\sqrt{(4 - 0)^2+(4 - 0)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66\)
For points \((4,4)\) and \((5,3)\):
\(d_2=\sqrt{(5 - 4)^2+(3 - 4)^2}=\sqrt{1+1}=\sqrt{2}\approx1.41\)

Step2: Calculate the perimeter of the rectangle

Since opposite sides of a rectangle are equal, the perimeter \(P = 2(d_1 + d_2)\)
\(P=2(5.66+1.41)=2\times7.07 = 14.14\approx14.1\)

Answer:

14.1