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)%0D%0A(%0D%0A0%0D%0A,%0D%0A0%0D%0A)%0D%0A, (4,4)%0D%0A(%0D%0A4%0D%0A,%0D%0A4%0D%0A)%0D%0A, (5,3)%0D%0A(%0D%0A5%0D%0A,%0D%0A3%0D%0A)%0D%0A, and (1,−1)%0D%0A(%0D%0A1%0D%0A,%0D%0A−%0D%0A1%0D%0A)%0D%0A? Round your answer to the nearest tenth.(1 point)%0D%0AThe perimeter is approximately units.

Answer 1

To find the perimeter of the rectangle with vertices at (0, 0), (4, 4), (5, 3), and (1, -1), we first need to confirm whether these points indeed form a rectangle and then calculate the lengths of two adjacent sides.

Step 1: Determine the vertices

We have the vertices:

1. A(0, 0)
2. B(4, 4)
3. C(5, 3)
4. D(1, -1)

Step 2: Calculate the lengths of the sides

Length of AB:

Using the distance formula: $$AB=\sqrt{(4-0{)}^2+(4-0{)}^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}\approx 5.7$$

Length of BC:

$$BC=\sqrt{(5-4{)}^2+(3-4{)}^2}=\sqrt{1+1}=\sqrt{2}\approx 1.4$$

Step 3: Calculate the perimeter

The perimeter (P) of a rectangle is given by: $$P=2\times (length+width)$$ Assuming AB as one side (length) and BC as the other (width): $$P=2\times (AB+BC)\approx 2\times (5.7+1.4)$$

Calculating the sum: $$5.7+1.4=7.1$$

Calculating the perimeter: $$P\approx 2\times 7.1=14.2$$

Final rounded answer

Thus, the perimeter of the rectangle is approximately 14.2 units.