Identify the line of reflection between the set of coordinates (1,6) and (5,6)

The line of reflection between the points \((1,6)\) and \((5,6)\) can be found by determining the line that is exactly halfway between these two points and is perpendicular to the line segment that joins them.

1. **Identify the midpoint** between \((1,6)\) and \((5,6)\):
   \[
   \text{Midpoint} = \left(\frac{1 + 5}{2}, \frac{6 + 6}{2}\right) = (3, 6)
   \]

2. **Determine the orientation**: Since both points have the same \(y\)-coordinate (6), they lie on a horizontal line.

3. **Find the line of reflection**: The line of reflection will be the vertical line passing through the midpoint \(x = 3\).

Therefore, the line of reflection is:
\[
x = 3
\]

Would you like more details or have any questions?

Here are some related questions:
1. How would you find the line of reflection between two points with different \(y\)-coordinates?
2. What is the process to find the midpoint for three-dimensional points?
3. How do you determine if two points are reflections over a specific line?
4. How can we generalize the line of reflection for points on different axes?
5. How does symmetry apply to reflections in coordinate geometry?

**Tip:** To find a line of reflection between two points with the same \(y\)-coordinate, look for a vertical line at the midpoint of their \(x\)-coordinates.

Learn how to identify the line of reflection between the points (1,6) and (5,6). This detailed solution covers concepts like midpoint calculation, line orientation, and symmetry. Suitable for students in Grades 7-9.

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