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To find the midpoint of the segment PQ, where \( P = (-3, 5) \) and \( Q = (1, 9) \), we use the midpoint formula:

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

Substitute the coordinates of \( P(x_1, y_1) = (-3, 5) \) and \( Q(x_2, y_2) = (1, 9) \) into the formula:

\[
M = \left( \frac{-3 + 1}{2}, \frac{5 + 9}{2} \right)
\]

Now, let's calculate:

\[
M = \left( \frac{-2}{2}, \frac{14}{2} \right) = (-1, 7)
\]

So, the midpoint of segment \( PQ \) is \( M = (-1, 7) \).

Would you like more details on this process or have any additional questions?

Here are five related questions for further practice:
1. What is the formula to find the distance between two points in a plane?
2. How would the midpoint change if \( P = (1, 5) \) and \( Q = (-3, -9) \)?
3. Can you find the slope of the line passing through points \( P \) and \( Q \)?
4. How do you find the equation of the line passing through two points?
5. How does the midpoint formula apply in three-dimensional space?

**Tip:** The midpoint formula always gives the point that is equidistant from both endpoints of the segment. It is a useful tool in geometry for finding the center of a line segment.

If P=(-3,5) and Q=(1,9), find the midpoint of segment PQ.

Learn how to find the midpoint of a line segment with given points P=(-3,5) and Q=(1,9) using the midpoint formula. This problem is a fundamental concept in coordinate geometry, suitable for students in Grades 6-8.

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