Question

1. build perseverance mrs. palmer is placing a retaining wall around a garden. the coordinates of the vertices of the wall are (1, 1), (1, 5), (6, 5), and (6, 1). if each grid square has a length of 2 feet, what is the perimeter of the garden? write an argument that can be used to justify your solution.

Explanation:

Step1: Find grid side lengths

Vertical side: $|5 - 1| = 4$ grid units
Horizontal side: $|6 - 1| = 5$ grid units

Step2: Convert to actual feet

Vertical length: $4 \times 2 = 8$ feet
Horizontal length: $5 \times 2 = 10$ feet

Step3: Calculate perimeter

Perimeter formula: $2 \times (length + width)$
Expression: $2 \times (10 + 8)$

Answer:

36 feet

Justification:

The vertices form a rectangle. First, calculate the side lengths in grid units using the difference in coordinates: vertical sides span 4 grid units, horizontal sides span 5 grid units. Multiply each by 2 feet per grid unit to get actual side lengths of 8 feet and 10 feet. Use the rectangle perimeter formula $2(l+w)$ to find the total perimeter is 36 feet.