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.