Question

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 square miles
12 square miles

8 square miles
8 square miles

−12
miles
negative 12 miles

12 miles
12 miles
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Answer 1

To find the dimensions and perimeter of rectangle ABCD with vertices A(1, -3), B(5, -3), C(5, -1), and D(1, -1), we’ll follow these steps:

1. Find the Length and Width:

   • The length is the distance between points A and B (horizontal distance).
   • The width is the distance between points A and D (vertical distance).

   Length (AB):

   • Coordinates of A: (1, -3)
   • Coordinates of B: (5, -3)
   • Length = x-coordinate of B - x-coordinate of A = 5 - 1 = 4 units

   Width (AD):

   • Coordinates of A: (1, -3)
   • Coordinates of D: (1, -1)
   • Width = y-coordinate of D - y-coordinate of A = -1 - (-3) = -1 + 3 = 2 units

2. Calculate the Perimeter:

   • The formula for the perimeter \(P\) of a rectangle is given by: \[ P = 2 \times (\text{Length} + \text{Width}) = 2 \times (4 + 2) = 2 \times 6 = 12 \text{ units} \]

Since the problem asks for the perimeter in miles, we can conclude that:

The perimeter of rectangle ABCD is 12 miles.

So, the correct response is 12 miles.