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

Question

has vertices point A (1,−3)
, point B (5, −3)
, point C (5, −1)
, and point D (1, −1)
.(1 point)
Responses

8 square miles
8 square miles

−12
miles
negative 12 miles

12 miles
12 miles

12 square miles

Answer 1

To find the perimeter of rectangle ABCD, we first need to determine the length and width of the rectangle using the coordinates of its vertices.

The vertices are:

• A (1, -3)
• B (5, -3)
• C (5, -1)
• D (1, -1)

Length and Width

1. Length: This can be determined by looking at the horizontal distance between points A and B (or points C and D):

   • Distance between A and B: \( |5 - 1| = 4 \)

2. Width: This can be determined by looking at the vertical distance between points A and D (or points B and C):

   • Distance between A and D: \( |-1 - (-3)| = |-1 + 3| = 2 \)

Perimeter Calculation

The formula for the perimeter \( P \) of a rectangle is: \[ P = 2 \times (\text{Length} + \text{Width}) \] Substituting the values we found: \[ P = 2 \times (4 + 2) = 2 \times 6 = 12 \text{ miles} \]

Conclusion

The perimeter of rectangle ABCD is 12 miles.

Thus, the correct response is: 12 miles