Question

On a coordinate plane, there are point at (negative 2, 1), (4, 1), (4, negative 3), and (negative 2, negative 3).
Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need?
4 feet
6 feet
10 feet
20 feet

Answer 1

To determine how many feet of stone Marina needs to surround the garden, we first calculate the perimeter of the rectangle defined by the points provided.

The points given are:
- A: (-2, 1)
- B: (4, 1)
- C: (4, -3)
- D: (-2, -3)

### Step 1: Calculate the lengths of the sides

1. **Width (horizontal distance):**
- The x-coordinates of points A and B are -2 and 4, respectively.
- Width = x-coordinate of B - x-coordinate of A = 4 - (-2) = 4 + 2 = 6 feet.

2. **Height (vertical distance):**
- The y-coordinates of points A and D are 1 and -3, respectively.
- Height = y-coordinate of A - y-coordinate of D = 1 - (-3) = 1 + 3 = 4 feet.

### Step 2: Calculate the perimeter of the rectangle

The formula for the perimeter \( P \) of a rectangle is:
\[
P = 2 \times (\text{Width} + \text{Height})
\]

Substituting the values we calculated:
\[
P = 2 \times (6 + 4) = 2 \times 10 = 20 \text{ feet}
\]

### Conclusion

Marina needs a total of **20 feet** of stone to surround the garden. Therefore, the answer is **20 feet**.