The midpoint *M* of *PQ* has coordinates (3.5, –4.5). Point *Q* has coordinates (–2, –6). Find the coordinates of point *P*.

*Write the coordinates as decimals or integers.*

To find the coordinates of point \( P(x_1, y_1) \), we can use the midpoint formula. The midpoint \( M \) of a segment with endpoints \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is given by:

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

Given:
- Midpoint \( M(3.5, -4.5) \)
- Point \( Q(-2, -6) \)

We can set up the following equations based on the midpoint formula:

1. \( \frac{x_1 + (-2)}{2} = 3.5 \)
2. \( \frac{y_1 + (-6)}{2} = -4.5 \)

### Step 1: Solve for \( x_1 \)

Multiply both sides of the first equation by 2:

\[
x_1 - 2 = 7
\]

Add 2 to both sides:

\[
x_1 = 9
\]

### Step 2: Solve for \( y_1 \)

Multiply both sides of the second equation by 2:

\[
y_1 - 6 = -9
\]

Add 6 to both sides:

\[
y_1 = -3
\]

### Final Answer:
The coordinates of point \( P \) are \( (9, -3) \).

Would you like more details or have any questions about the steps?

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Here are five related questions:
1. How would the midpoint change if point \( P \) was moved further away from \( Q \)?
2. What is the distance between points \( P \) and \( Q \)?
3. Can you find the slope of the line passing through points \( P \) and \( Q \)?
4. How would you find the coordinates of a point that divides the segment \( PQ \) in a different ratio?
5. What are the coordinates of the midpoint if \( Q \) were at \( (-5, 2) \)?

**Tip:** Always verify your answers by substituting the coordinates back into the midpoint formula to check for consistency.

Learn how to find the coordinates of point P using the midpoint formula, given midpoint M(3.5, -4.5) and point Q(-2, -6). Detailed step-by-step solution provided.

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