To calculate the perimeter of the rectangle, we need to first determine the dimensions of the rectangle. The rectangle is defined by the coordinates of its corners.
The points given are:
- A (3, 4)
- B (7, 2)
- C (1, 1)
- D (-3, 1)
However, based on the coordinates, we need to identify the pairs of points that represent opposite corners of the rectangle.
To find the lengths of the sides of the rectangle, we can identify the maximum and minimum values for the x-coordinates and y-coordinates:
-
The x-coordinates are 3, 7, 1, -3:
- Maximum x: 7 (from point B)
- Minimum x: -3 (from point D)
-
The y-coordinates are 4, 2, 1, 1:
- Maximum y: 4 (from point A)
- Minimum y: 1 (from points C and D)
From this information, we can find the lengths of the sides:
-
Length of the rectangle (width):
- \( \text{Width} = \text{Max x} - \text{Min x} = 7 - (-3) = 7 + 3 = 10 \text{ inches} \)
-
Length of the rectangle (height):
- \( \text{Height} = \text{Max y} - \text{Min y} = 4 - 1 = 3 \text{ inches} \)
Now we can calculate the perimeter \( P \) of the rectangle using the formula: \[ P = 2 \times (\text{Width} + \text{Height}) \] Substituting the dimensions: \[ P = 2 \times (10 + 3) = 2 \times 13 = 26 \text{ inches} \]
Thus, the perimeter of the rectangle is \( \boxed{26} \) inches.