We are given that the midpoint of segment $PQ$ is $(6, -8)$, and the coordinates of point $Q$ are $(-5, -12)$. We need to find the coordinates of point $P(x_1, y_1)$.

The formula for the midpoint of a segment is: $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ where $(x_1, y_1)$ are the coordinates of point $P$, and $(x_2, y_2)$ are the coordinates of point $Q$.

Using the given midpoint $(6, -8)$ and $Q(-5, -12)$, we can set up the following equations:

$\frac{x_1 + (-5)}{2} = 6$ $\frac{y_1 + (-12)}{2} = -8$

Solving for $x_1$:

$\frac{x_1 - 5}{2} = 6$ Multiply both sides by 2: $x_1 - 5 = 12$ Add 5 to both sides: $x_1 = 17$

Solving for $y_1$:

$\frac{y_1 - 12}{2} = -8$ Multiply both sides by 2: $y_1 - 12 = -16$ Add 12 to both sides: $y_1 = -4$

Thus, the coordinates of point $P$ are $(17, -4)$.

Do you need further clarification or details? Here are some related questions for practice:

1. What is the formula for the midpoint of a segment?
2. How do you find the distance between two points?
3. If $Q(3, 5)$ and $P(7, 9)$, what is the midpoint of segment $PQ$?
4. What is the slope of the line passing through points $P(17, -4)$ and $Q(-5, -12)$?
5. Can a line segment have a negative midpoint?

Tip: Always remember, the midpoint is simply the average of the x-coordinates and y-coordinates of the two points.