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