Question

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?

Explanation:

Step1: Find the length of the horizontal sides

The horizontal distance from \(x = 10\) to \(x = 100\) is \(100 - 10=90\) units.

Step2: Find the length of the vertical sides

The vertical distance from \(y = 10\) to \(y = 80\) is \(80 - 10 = 70\) units.

Step3: Calculate the perimeter of the rectangle - like shape (using the formula \(P=2(l + w)\))

The formula for the perimeter of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Substituting \(l = 90\) and \(w = 70\), we get \(P=2(90 + 70)\).
First, calculate inside the parentheses: \(90+70 = 160\). Then multiply by 2: \(P=2\times160=320\) units.

Step4: Convert units to yards

Since each unit represents 10 yards, multiply the perimeter in units by 10. So, \(320\times10\) yards.

Answer:

\(3200\) yards