The **missing endpoint formula** is used when you know one endpoint of a line segment and the midpoint, and you want to find the other endpoint.

Let’s break this down step by step:

Given:
- One endpoint \( A(x_1, y_1) \)
- The midpoint \( M(x_m, y_m) \)
- The unknown endpoint \( B(x_2, y_2) \)

The midpoint formula is:

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

To find the missing endpoint \( B(x_2, y_2) \), solve for \( x_2 \) and \( y_2 \) using the following formulas:

\[
x_2 = 2x_m - x_1
\]
\[
y_2 = 2y_m - y_1
\]

### Example:
If the given endpoint is \( A(3, 4) \) and the midpoint is \( M(6, 8) \), you can find the other endpoint \( B(x_2, y_2) \) as follows:

\[
x_2 = 2 \times 6 - 3 = 12 - 3 = 9
\]
\[
y_2 = 2 \times 8 - 4 = 16 - 4 = 12
\]

Thus, the missing endpoint \( B \) is \( (9, 12) \).

Would you like more details or any further explanation on this?

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Here are five related questions to expand your understanding:
1. How do you calculate the midpoint of a line segment?
2. What is the difference between the midpoint formula and the distance formula?
3. How would you find the equation of a line segment given both endpoints?
4. Can the missing endpoint formula be applied in three dimensions?
5. How would you calculate the length of a line segment between two points?

**Tip**: The midpoint formula is just the average of the corresponding coordinates of the endpoints!

Learn how to find a missing endpoint of a line segment using the midpoint formula. This example covers essential concepts in coordinate geometry, including step-by-step calculations of coordinates based on one known endpoint and the midpoint. Suitable for students in Grades 8-10.

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