Questions: Distance and Midpoint Assessment: Use the mall layout to answer the following questions. Use the given grid to find order pairs that can be used to show all computations that led you to your solutions. Appropriate formulas must be used as part of mathematical computations. The black dots represent doorways (6,9), (9,9), (15,9) and (15,6). Identify the coordinates of the doorway of your Pretzel shop by selecting two stores that would give you a midpoint that would fall in the region of the rectangular area. Be sure to include mathematical computations that lead your answer.

Distance and Midpoint Assessment: Use the mall layout to answer the following questions. Use the given grid to find order pairs that can be used to show all computations that led you to your solutions. Appropriate formulas must be used as part of mathematical computations. The black dots represent doorways (6,9), (9,9), (15,9) and (15,6). Identify the coordinates of the doorway of your Pretzel shop by selecting two stores that would give you a midpoint that would fall in the region of the rectangular area. Be sure to include mathematical computations that lead your answer.
Transcript text: Distance and Midpoint Assessment: Use the mall layout to answer the following questions. Use the given grid to find order pairs that can be used to show all computations that led you to your solutions. Appropriate formulas must be used as part of mathematical computations. The black dots represent doorways $6),(9,9),(15,9)$ and $(15,6)$. Identify the coordinates of the doorway of your Pretzel shop by selecting two stores that would give you a midpoint that would fall in the region of the rectangular area. Be sure to include mathematical computations that lead your answer.
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Solution

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Solution Steps

Step 1: Finding suitable store doorways

The Pretzel shop will be located within the rectangle with vertices (9, 6), (9, 9), (15, 9), and (15, 6). We need to select two existing store doorways that, when a midpoint is calculated, will fall within this rectangle. Visually inspecting the map, the "Party Store" doorway at (6,7) and the "Shoes Express" doorway at (20,11) appear to be good candidates.

Step 2: Calculating the midpoint

The midpoint formula is: ((x₁ + x₂)/2, (y₁ + y₂)/2).

Using the coordinates for the "Party Store" (6, 7) and "Shoes Express" (20, 11):

Midpoint = ((6 + 20)/2, (7 + 11)/2) = (26/2, 18/2) = (13, 9)

Step 3: Verifying the midpoint

The calculated midpoint (13, 9) falls within the defined rectangular area of the Pretzel shop (9≤x≤15 and 6≤y≤9) since 9 ≤ 13 ≤ 15 and 6 ≤ 9 ≤ 9.

Final Answer:

The Pretzel shop doorway can be located at (13, 9) by selecting the "Party Store" and the "Shoes Express" doorways and using their midpoint.

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