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**.