To solve this problem, we need to calculate the straight-line distance between Penny's house and Akiko's house, as shown on the grid map. Each square on the grid represents one block, and the bottom left corner of the grid is the origin (0, 0).

Approach:

1. Identify the coordinates of Penny's and Akiko's houses on the grid.
   • Based on the map, estimate the positions of Penny and Akiko in terms of how many blocks they are from the origin.
2. Use the distance formula to calculate the straight-line distance between these two points.

The distance formula is: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ where:

• $(x_1, y_1)$ are the coordinates of Penny's house.
• $(x_2, y_2)$ are the coordinates of Akiko's house.

Let me process the coordinates and compute the distance.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still use the coordinates of Penny's and Akiko's houses that I estimated as (2, 8) and (8, 2), respectively, and apply the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let me know if you need more details or further assistance!

Here are 5 related questions to think about:

1. How does changing the positions of Penny and Akiko affect the distance?
2. How can you apply the distance formula to real-world situations?
3. What would happen if each block on the map represented 2 units instead of 1?
4. Can you calculate the time it might take to walk this distance if you knew the speed?
5. How could you use this formula in three-dimensional space?

Tip: The distance formula is a direct application of the Pythagorean theorem for two points on a plane!