Fina the midpoint of the line segment whose endpoints are
4 3
,
5 4
    −
 
and
3 5
,
10 6
    − −
 

To find the midpoint of a line segment whose endpoints are given, we use the midpoint formula. The formula for the midpoint \((M)\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Given endpoints:
\[
\left( 4, 5 \right) \text{ and } \left( 3, 10 \right)
\]
\[
\left( 3, -4 \right) \text{ and } \left( -5, -6 \right)
\]

Plugging in the values:

1. For the first coordinate pair \((4, 5)\) and \((3, 10)\):

\[
M_x = \frac{4 + 3}{2} = \frac{7}{2} = 3.5
\]

\[
M_y = \frac{5 + 10}{2} = \frac{15}{2} = 7.5
\]

2. For the second coordinate pair \((3, -4)\) and \((-5, -6)\):

\[
M_x = \frac{3 + (-5)}{2} = \frac{-2}{2} = -1
\]

\[
M_y = \frac{-4 + (-6)}{2} = \frac{-10}{2} = -5
\]

So, the midpoints of the line segments are:

\[
M = \left(3.5, 7.5 \right) \text{ and } M = \left(-1, -5\right)
\]

Do you want any details or have any questions?

Here are 5 related questions:
1. How is the midpoint used in geometry?
2. How would you find the midpoint in three-dimensional space?
3. What is the significance of the midpoint in coordinate geometry?
4. Can the midpoint formula be used in real-world applications?
5. How does the distance formula relate to the midpoint formula?

**Tip:** Always double-check your coordinates when applying the midpoint formula to ensure accuracy!

Learn how to find the midpoint of a line segment with given endpoints using the midpoint formula. This problem covers coordinate geometry concepts and provides step-by-step calculations for accurate results. Suitable for students in Grades 7-9.

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