The midpoint of CD is M(3, 6). One endpoint is D(5, 10). Find the coordinates of the other endpoint C.

Write the coordinates as decimals or integers.


Given the midpoint \( M(3, 6) \) and one endpoint \( D(5, 10) \), we can find the coordinates of the other endpoint \( C(x_1, y_1) \) using the midpoint formula:

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

Given:
- \( M = (3, 6) \)
- \( D = (5, 10) \)
- \( C = (x_1, y_1) \)

The midpoint formula gives us two equations:

\[
\frac{x_1 + 5}{2} = 3
\]

\[
\frac{y_1 + 10}{2} = 6
\]

### Solve for \( x_1 \):
\[
\frac{x_1 + 5}{2} = 3
\]
Multiply both sides by 2:
\[
x_1 + 5 = 6
\]
Subtract 5 from both sides:
\[
x_1 = 1
\]

### Solve for \( y_1 \):
\[
\frac{y_1 + 10}{2} = 6
\]
Multiply both sides by 2:
\[
y_1 + 10 = 12
\]
Subtract 10 from both sides:
\[
y_1 = 2
\]

### Final Answer:
The coordinates of the other endpoint \( C \) are \( \boxed{(1, 2)} \).

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the midpoint if both endpoints are known?
2. How does the distance formula relate to finding midpoints?
3. What happens if the midpoint is known but both endpoints are unknown?
4. Can the midpoint formula be used in three dimensions?
5. How can you verify your solution is correct using another method?

**Tip:** When working with midpoint problems, remember that the midpoint coordinates are the average of the corresponding coordinates of the endpoints.

The midpoint of CD is M(3, 6). One endpoint is D(5, 10). Find the coordinates of the other endpoint C. Write the coordinates as decimals or integers.

Learn how to find the coordinates of the other endpoint C when the midpoint M(3, 6) and one endpoint D(5, 10) are given. This problem uses the midpoint formula and covers key coordinate geometry concepts. Suitable for students in Grades 6-8.

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