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?

---

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.