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Scout Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two.
The camp designers decide they need another set of cabins.  If they want the Mess Hall to be the midpoint of the two sets of cabins, what should the coordinate location of the new cabins?

To solve this problem, let's break it down into two steps:

1. **Identify the coordinates of the Mess Hall and the current Cabins from the grid.**
2. **Determine the coordinates of the new cabins so that the Mess Hall becomes the midpoint between the two sets of cabins.**

### Step 1: Identifying Coordinates
- From the grid, the Mess Hall is located at approximately (-3, -2).
- The Cabins are located at (5, 4).

### Step 2: Finding the New Cabins Coordinates
For the Mess Hall to be the midpoint between the current Cabins and the new cabins, we can use the midpoint formula. The midpoint formula is given by:

\[
\text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

Here, the coordinates of the Mess Hall should equal the midpoint between the coordinates of the old cabins (5, 4) and the new cabins \((x, y)\). Therefore, setting the coordinates of the midpoint equal to (-3, -2), we get the following equations:

\[
\frac{5 + x}{2} = -3 \quad \text{and} \quad \frac{4 + y}{2} = -2
\]

We can solve these two equations to find \(x\) and \(y\), the coordinates of the new cabins.

### Solving for \(x\):
\[
\frac{5 + x}{2} = -3
\]
Multiply both sides by 2:
\[
5 + x = -6
\]
Subtract 5 from both sides:
\[
x = -11
\]

### Solving for \(y\):
\[
\frac{4 + y}{2} = -2
\]
Multiply both sides by 2:
\[
4 + y = -4
\]
Subtract 4 from both sides:
\[
y = -8
\]

### Final Answer
The coordinates of the new cabins should be \((-11, -8)\).

Would you like further details or have any questions?

### Related Questions:
1. How do you find the midpoint of two points on a coordinate plane?
2. What is the formula for finding the distance between two points?
3. How could we verify the midpoint location using the grid?
4. If the new cabins moved 2 units up, what would be the new midpoint?
5. What are the implications of shifting both sets of cabins but keeping the midpoint constant?

### Tip:
Always double-check the grid coordinates visually to ensure accuracy when solving geometric problems.

Learn how to find the coordinates of new cabins using the midpoint formula in coordinate geometry. This problem involves mapping locations on a coordinate grid and calculating the midpoint between two sets of points. Suitable for Grades 6-8.

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