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?
If points T and T′ have the same x-coordinate, it means that the line of reflection is vertical and passes through the y-axis. This is because the x-coordinate remains the same after reflection, implying that the line of reflection is perpendicular to the x-axis.
The line of reflection is the y-axis.
options are
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.
If points T and T' have the same x-coordinate after reflecting point T over a line of reflection, it means that the line of reflection is vertical and parallel to the y-axis. In other words, the line of reflection is a vertical line passing through the x-coordinate of point T.
To determine what must be true when reflecting a point T over a line of reflection, resulting in point T', and when T and T' have the same x-coordinate, we need to understand reflection in geometry.
Reflection is a geometric transformation that flips a figure over a specific line called the line of reflection. When a point is reflected over a line, the image point is equidistant from the line of reflection as the original point.
For point T to have the same x-coordinate as point T', it means that the reflection line must be vertical. This is because the x-coordinate represents the horizontal position of a point on a coordinate plane, and if T and T' have the same x-coordinate, it means they lie on the same vertical line.
Alternatively, if T and T' have the same x-coordinate, it means the line of reflection must be a vertical line passing through the x-coordinate of point T. In other words, the line of reflection is a vertical line that goes through the x-coordinate of point T.
In summary, if points T and T' have the same x-coordinate, it implies that the line of reflection is vertical and passes through the x-coordinate of point T.