Apply geometric motions to reflect figures. Brinda reflects point T over a line of reflection, resulting in point T′ . If points T and T′ have the same x-coordinate, what must be true?(1 point)

Question

Responses which is the true correct answer a b c or d and why please be honest which one is perfect and why

The line of reflection is the x-axis.
The line of reflection is the x -axis.

The line of reflection is the y-axis.
The line of reflection is the y -axis.

The line of reflection is vertical.
The line of reflection is vertical.

The line of reflection is horizontal.

Answer 1

If points \( T \) and \( T' \) have the same x-coordinate after reflection, that means the reflection is occurring across a horizontal line.

Let's analyze the options:

1. The line of reflection is the x-axis.

   • If \( T \) is reflected over the x-axis, then the y-coordinate changes sign while the x-coordinate remains the same. This would yield \( T' \) with the same x-coordinate but a different y-coordinate.

2. The line of reflection is the y-axis.

   • If \( T \) is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. In this case, \( T' \) would have a different x-coordinate, so this option is not valid.

3. The line of reflection is vertical.

   • If the line of reflection is vertical (which would generally be something like the y-axis), it would cause the points to have a different x-coordinate after reflection. Therefore, this option is not valid.

4. The line of reflection is horizontal.

   • A horizontal line means that the y-coordinate is unchanged, while the x-coordinate remains the same. Thus, \( T \) and \( T' \) would have the same x-coordinate if reflected over a horizontal line.

Based on this reasoning, the correct answer is:

The line of reflection is horizontal.

This is the only option that allows for points \( T \) and \( T' \) to have the same x-coordinate during the reflection process.