https://file.aiquickdraw.com/mathbot/file/1727713879011yip4uhy6.jpg

The problem asks for the coordinates of the midpoint \( M \) of a line segment \( AB \), where the endpoints are \( A(6, -1) \) and \( B(-6, -6) \).

To find the midpoint \( M(x_m, y_m) \) of a line segment, we use the midpoint formula:

\[
x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}
\]

### Given:
- \( A(6, -1) \)
- \( B(-6, -6) \)

#### Step 1: Apply the formula to the \( x \)-coordinates:
\[
x_m = \frac{6 + (-6)}{2} = \frac{0}{2} = 0
\]

#### Step 2: Apply the formula to the \( y \)-coordinates:
\[
y_m = \frac{-1 + (-6)}{2} = \frac{-7}{2} = -3.5
\]

Thus, the coordinates of the midpoint \( M \) are:
\[
M(0, -3.5)
\]

This matches the answer provided in the image.

---

Do you want more details or have any questions? 

Here are 5 related questions to deepen your understanding:
1. How would you find the length of the line segment \( AB \)?
2. What is the slope of the line passing through points \( A \) and \( B \)?
3. How does the midpoint formula work in three dimensions?
4. How do you find the equation of the line passing through points \( A \) and \( B \)?
5. How would the midpoint change if one of the coordinates was shifted?

**Tip**: The midpoint formula can be extended to find midpoints in higher dimensions (3D or more) by averaging each corresponding coordinate pair!

The endpoints of AB are A(6, -1) and B(-6, -6). Find the coordinates of the midpoint M.

This problem demonstrates how to find the midpoint of a line segment with endpoints A(6, -1) and B(-6, -6) using the midpoint formula. The solution applies basic coordinate geometry concepts, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation