If 
(6, −8)
 is the midpoint of segment PQ and the coordinates of Q are 
(−5, −12),
 find the coordinates of P

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.

If (6, −8) is the midpoint of segment PQ and the coordinates of Q are (−5, −12), find the coordinates of P.

Solve the problem of finding the coordinates of point P when the midpoint is (6, -8) and point Q is (-5, -12). This step-by-step solution covers the midpoint formula and algebraic manipulation, ideal for students in Grades 8-10.

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