https://file.aiquickdraw.com/mathbot/file/17263159292851881hina.jpg

Yes, I can help you solve this!

The problem provides the following information:
- The midpoint \( M \) of the line segment \( GH \) is \( M(8, 0) \).
- One endpoint \( H \) of the segment is \( H(-2, 9) \).
- We need to find the coordinates of the other endpoint \( G(x_2, y_2) \).

To find the coordinates of the other endpoint, we can use the midpoint formula. The formula for the midpoint \( M \) of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Given:
- Midpoint \( M(8, 0) \),
- Endpoint \( H(-2, 9) \), which means \( x_1 = -2 \) and \( y_1 = 9 \),
- We need to solve for the unknown endpoint \( G(x_2, y_2) \).

### Solving for \( x_2 \) and \( y_2 \):

1. **Solve for \( x_2 \)** using the x-coordinates:
   \[
   \frac{x_1 + x_2}{2} = 8
   \]
   Substitute \( x_1 = -2 \):
   \[
   \frac{-2 + x_2}{2} = 8
   \]
   Multiply both sides by 2:
   \[
   -2 + x_2 = 16
   \]
   Add 2 to both sides:
   \[
   x_2 = 18
   \]

2. **Solve for \( y_2 \)** using the y-coordinates:
   \[
   \frac{y_1 + y_2}{2} = 0
   \]
   Substitute \( y_1 = 9 \):
   \[
   \frac{9 + y_2}{2} = 0
   \]
   Multiply both sides by 2:
   \[
   9 + y_2 = 0
   \]
   Subtract 9 from both sides:
   \[
   y_2 = -9
   \]

### Final Answer:
The coordinates of the other endpoint \( G \) are \( G(18, -9) \).

Let me know if you would like more details or explanations.

Here are 5 related questions to expand your understanding:
1. What is the midpoint formula used for finding midpoints between two points?
2. How would you find the distance between two points on a plane?
3. How can you find the slope of a line using two endpoints?
4. How is the midpoint formula related to the average of two values?
5. How would you generalize the formula for 3D space?

**Tip:** Always make sure to double-check signs when dealing with midpoint problems to avoid errors with addition or subtraction!

The coordinates of the midpoint of GH are M(8, 0) and the coordinates of one endpoint are H(-2, 9). The coordinates of the other endpoint are (__, __).

Learn how to find the coordinates of the other endpoint of a line segment given the midpoint M(8, 0) and one endpoint H(-2, 9). This problem involves the midpoint formula and is suitable for students in Grades 8-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation