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Find the other endpoint of the line segment with the given endpoint and midpoint. 

To find the other endpoint of a line segment given one endpoint and the midpoint, we can use the midpoint formula, which states:

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

Where:
- \( M \) is the midpoint
- \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the endpoints

In this case:
- One endpoint is \( (-8, -13) \)
- The midpoint is \( (-10, 3) \)
- We need to find the other endpoint \( (x_2, y_2) \)

Using the midpoint formula, we can set up the following equations:

\[
-10 = \frac{-8 + x_2}{2} \quad \text{(for the x-coordinate)}
\]
\[
3 = \frac{-13 + y_2}{2} \quad \text{(for the y-coordinate)}
\]

Now, solving for \( x_2 \) and \( y_2 \):

1. Multiply both sides of the equation by 2 to eliminate the fraction:
\[
-10 \times 2 = -8 + x_2 \quad \Rightarrow \quad -20 = -8 + x_2
\]
Solve for \( x_2 \):
\[
x_2 = -20 + 8 = -12
\]

2. For the y-coordinate:
\[
3 \times 2 = -13 + y_2 \quad \Rightarrow \quad 6 = -13 + y_2
\]
Solve for \( y_2 \):
\[
y_2 = 6 + 13 = 19
\]

Thus, the other endpoint is \( (-12, 19) \).

Answer: \((-12, 19)\)

Would you like more details on the steps? Here are some related questions you can explore:

1. How do you find the midpoint if both endpoints are given?
2. What is the significance of the midpoint in geometry?
3. How can you use the distance formula to find the length of the line segment between two points?
4. What happens if the midpoint and both endpoints are the same point?
5. How do you extend this process to three-dimensional geometry?

**Tip:** To check your work, plug the endpoint coordinates back into the midpoint formula and verify that you get the correct midpoint!

Find the other endpoint of the line segment with the given endpoint (-8, -13) and midpoint (-10, 3).

Learn how to find the other endpoint of a line segment given one endpoint (-8, -13) and the midpoint (-10, 3). This step-by-step solution covers key geometric concepts, including the midpoint formula. Suitable for students in Grades 8-10.

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