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 horizontal.
The line of reflection is horizontal.

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.

Answer 1

When point T is reflected over a line of reflection, and the resulting point T′ has the same x-coordinate as point T, it indicates the vertical alignment of these points.

For the reflection of point T (with coordinates \((x, y)\)) to result in point T′ (with coordinates \((x, y′)\)) having the same x-coordinate, it means that the line of reflection must be a vertical line. This is because vertical reflection maintains the x-coordinates while potentially changing the y-coordinates.

Therefore, the correct answer is:

The line of reflection is vertical.

This is because a vertical line will not change the x-coordinate of point T when reflecting it, while potentially altering its y-coordinate.