Given the endpoint \((-7, -7)\) and the midpoint \((-1, -8)\), we can find the other endpoint using the midpoint formula:

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

Let the other endpoint be \((x, y)\).

Using the midpoint formula:

\[
\left( \frac{-7 + x}{2}, \frac{-7 + y}{2} \right) = (-1, -8)
\]

This gives us two equations:

\[
\frac{-7 + x}{2} = -1 \quad \text{and} \quad \frac{-7 + y}{2} = -8
\]

Let's solve these:

1. Solve for \(x\):

\[
\frac{-7 + x}{2} = -1
\]

Multiply both sides by 2:

\[
-7 + x = -2
\]

Add 7 to both sides:

\[
x = 5
\]

2. Solve for \(y\):

\[
\frac{-7 + y}{2} = -8
\]

Multiply both sides by 2:

\[
-7 + y = -16
\]

Add 7 to both sides:

\[
y = -9
\]

So, the other endpoint is \((5, -9)\).

Would you like more details or have any other questions?

### Related Questions:
1. How do you verify the midpoint of a line segment given both endpoints?
2. What is the geometric interpretation of a midpoint?
3. How can you determine the equation of a line given the midpoint and one endpoint?
4. How do you find the distance between the midpoint and an endpoint?
5. How do you find the coordinates of a point that divides a segment in a given ratio?
6. What is the process for finding the slope of a line given two endpoints?
7. How can you determine the length of a line segment in a coordinate plane?
8. What are the applications of the midpoint formula in real-world problems?

**Tip:** When solving problems involving the midpoint formula, carefully solve the system of equations for each coordinate to avoid errors.

Learn how to find the other endpoint of a line segment given one endpoint and the midpoint. This problem involves using the midpoint formula and solving equations. Suitable for high school students studying coordinate geometry.

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