P(8, 5) and Q(5, –7) are the endpoints of a line segment. What is the midpoint M of that line segment?

Write the coordinates as decimals or integers.


The formula for the midpoint \( M \) of a line segment with endpoints \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is:

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

Given the endpoints \( P(8, 5) \) and \( Q(5, -7) \), we can substitute the coordinates into the midpoint formula:

\[
M = \left( \frac{8 + 5}{2}, \frac{5 + (-7)}{2} \right)
\]

\[
M = \left( \frac{13}{2}, \frac{-2}{2} \right)
\]

\[
M = (6.5, -1)
\]

Thus, the midpoint \( M \) of the line segment is \( (6.5, -1) \).

Would you like more details on how midpoint formulas work or have any further questions?

Here are 5 related questions to explore:
1. How do you calculate the distance between two points on a coordinate plane?
2. What is the slope of the line passing through the points \( P(8, 5) \) and \( Q(5, -7) \)?
3. How do you find the equation of the line that passes through two points?
4. What happens if both endpoints of the segment have the same x-coordinates?
5. Can the midpoint formula be extended to three dimensions for 3D geometry?

**Tip**: Remember, the midpoint is always the average of the coordinates of the endpoints!

P(8, 5) and Q(5, –7) are the endpoints of a line segment. What is the midpoint M of that line segment?

Learn how to find the midpoint of a line segment with endpoints P(8, 5) and Q(5, -7). This problem demonstrates the midpoint formula and provides a step-by-step solution suitable for students in Grades 6-8.

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