Question

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)
Responses which answer is the true correct answer and why just eliminate the ones that arne't correct and tell me 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

To determine which statement is true regarding the reflection of point T over a line of reflection resulting in point T′, where T and T′ have the same x-coordinate, we need to consider the nature of reflection.

When a point is reflected over a line, the distance from the original point to the line is the same as the distance from the reflected point to the line.

1. **The line of reflection is the x-axis.**
- **False.** If T and T′ have the same x-coordinate and are reflected over the x-axis, they would have different y-coordinates (the y-coordinate of T would become negative if it were positive, and vice versa). This means the x-coordinates would not remain the same unless the point is located exactly on the x-axis.

2. **The line of reflection is the y-axis.**
- **True.** If T and T′ have the same x-coordinate, then reflecting over the y-axis would result in having the same x-coordinate. The y-coordinates can differ, but the x-coordinate remains the same, which is consistent with the information given.

3. **The line of reflection is vertical.**
- **True.** If T and T′ have the same x-coordinate, this implies that the reflection is across a vertical line (like the y-axis), which means they would remain at the same x-coordinate regardless of the differences in their y-coordinates.

4. **The line of reflection is horizontal.**
- **False.** If the line of reflection were horizontal, then reflecting T would change the y-coordinate and not keep the same x-coordinate. Hence T and T′ would not have the same x-coordinate in this case.

In conclusion, the correct statements are that the line of reflection is the y-axis and the line of reflection is vertical, while the other two options (the x-axis and horizontal lines) are incorrect.