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 answer is correct and why

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

The line of reflection is horizontal.

Answer 1

If points T and T′ have the same x-coordinate after the reflection, that means they are positioned vertically with respect to one another. This indicates that the line of reflection must be horizontal, as reflecting a point vertically across a horizontal line does not change its x-coordinate.

Therefore, the correct answer is:

The line of reflection is horizontal.

Here's the reasoning:

• When a point is reflected over a horizontal line (like the x-axis), the y-coordinate changes (it becomes the opposite of the original), while the x-coordinate remains the same.
• Since T and T′ have the same x-coordinate, they must be symmetric with respect to a horizontal line of reflection.

So, T and T′ sharing the same x-coordinate confirms that the line of reflection is indeed horizontal.