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We need to find the perimeter of the garden outlined in the coordinate plane.

### Step 1: List the vertices of the garden from the graph:
- (10, 80)
- (100, 80)
- (100, 30)
- (70, 30)
- (70, 10)
- (40, 10)
- (40, 30)
- (10, 30)

Each grid unit represents 10 yards, so we will calculate the distance between the consecutive vertices and then sum them up.

### Step 2: Calculate the distances between the vertices:
1. From (10, 80) to (100, 80): The change in x is \( 100 - 10 = 90 \) units. Since each unit is 10 yards, the length is \( 90 \times 10 = 900 \) yards.
2. From (100, 80) to (100, 30): The change in y is \( 80 - 30 = 50 \) units, which gives \( 50 \times 10 = 500 \) yards.
3. From (100, 30) to (70, 30): The change in x is \( 100 - 70 = 30 \) units, so \( 30 \times 10 = 300 \) yards.
4. From (70, 30) to (70, 10): The change in y is \( 30 - 10 = 20 \) units, so \( 20 \times 10 = 200 \) yards.
5. From (70, 10) to (40, 10): The change in x is \( 70 - 40 = 30 \) units, giving \( 30 \times 10 = 300 \) yards.
6. From (40, 10) to (40, 30): The change in y is \( 30 - 10 = 20 \) units, giving \( 20 \times 10 = 200 \) yards.
7. From (40, 30) to (10, 30): The change in x is \( 40 - 10 = 30 \) units, so \( 30 \times 10 = 300 \) yards.
8. From (10, 30) to (10, 80): The change in y is \( 80 - 30 = 50 \) units, giving \( 50 \times 10 = 500 \) yards.

### Step 3: Add all the lengths:
\[
900 + 500 + 300 + 200 + 300 + 200 + 300 + 500 = 3200 \text{ yards}
\]

Thus, Martin needs **3200 yards** of rope to rope off the perimeter of the garden.

Would you like further clarification or details?

### Follow-up Questions:
1. How would the calculation change if each unit on the grid represented 5 yards?
2. Can you calculate the area of this garden using coordinate geometry?
3. How would you find the length of the rope if the garden's shape changed?
4. Could the perimeter be found using a different method, such as vector analysis?
5. How can you use the perimeter formula for other polygon shapes?

### Tip:
Always double-check the distances between points on a coordinate plane by calculating changes in x and y coordinates carefully.

Martin used a coordinate plane to design the garden shown. Each unit on the grid represents 10 yards. How many yards of rope does Martin need to rope off the perimeter of the garden?

Learn how to calculate the perimeter of a garden designed on a coordinate plane. The garden's vertices are given, and each unit on the grid represents 10 yards. Find the total length of rope required to fence the garden by applying basic distance and perimeter formulas.

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