Question

Apply the techniques of using the coordinates to find the length and the width of the polygon. Use the length and the width to find the perimeter of the polygon in miles. Rectangle ABCD
has vertices point A (1,−3)
, point B (5, −3)
, point C (5, −1)
, and point D (1, −1)
.(1 point)
Responses

−12
miles
negative 12 miles

12 miles
12 miles

8 square miles
8 square miles

12 square miles
12 square miles

Answer 1

To find the length and width of rectangle ABCD, we will first identify the coordinates of the vertices:

- Point A: (1, -3)
- Point B: (5, -3)
- Point C: (5, -1)
- Point D: (1, -1)

**Step 1: Calculate the Length**

The length of the rectangle can be determined by the distance between points A and B, which are on the same horizontal line (y-coordinates are equal).

Length \( L \) = \( x_B - x_A \)

- \( L = 5 - 1 = 4 \) units

**Step 2: Calculate the Width**

The width of the rectangle can be determined by the distance between points A and D, which are on the same vertical line (x-coordinates are equal).

Width \( W \) = \( y_D - y_A \)

- \( W = -1 - (-3) = -1 + 3 = 2 \) units

**Step 3: Calculate the Perimeter**

The perimeter \( P \) of a rectangle is given by the formula:

\[ P = 2(L + W) \]

Substituting the values we found for length and width:

\[ P = 2(4 + 2) = 2(6) = 12 \text{ units} \]

**Step 4: Convert to miles**

Assuming that the unit used is in miles, since the problem asks for the perimeter in miles, we can state:

- The perimeter of rectangle ABCD is **12 miles**.

Therefore, the correct answer from the options provided is:

**12 miles**