A geometric figure is reflected over the y-axis. Which of the following best describes this transformation?
A. The figure is flipped across a line, producing a mirror image.
B. The figure turns around the point, changing the orientation of its points relative to the point.
C. The figure is moved from one position to another while maintaining its orientation.
D. The figure is stretched away from the point.
Answer (2)
When a geometric figure is reflected over the y-axis, the transformation that occurs is known as a reflection. A reflection over the y-axis specifically involves flipping the figure across the y-axis, which acts as a line of reflection.
Here's a step-by-step explanation of what happens in this transformation:
Line of Reflection : In this case, the y-axis is the line of reflection. This means that every point of the reflected figure will be mirrored on the opposite side of the y-axis.
Mirror Image : The original figure is flipped to produce a mirror image on the opposite side of the y-axis. This means that points on the original figure will have the same distance from the y-axis as their corresponding points on the reflected figure.
Coordinates Change : If you consider a point on the original figure with coordinates ( x , y ) , its reflection over the y-axis will have coordinates ( − x , y ) . Here, the x-coordinate is negated, while the y-coordinate remains the same, which results in the flipping of the figure.
Among the given options, "The figure is flipped across a line, producing a mirror image" best describes this transformation, as it accurately captures the essence of what occurs during a reflection over the y-axis.
To sum up, reflection over the y-axis results in producing a mirror image by swapping the side of each point relative to the y-axis while maintaining the same distance from it.
Therefore, the correct answer is:
The figure is flipped across a line, producing a mirror image.
The transformation of reflecting a geometric figure over the y-axis is known as a reflection, where the figure is flipped to create a mirror image. The coordinates of points on the original figure change from ( x , y ) to ( − x , y ) . Therefore, the correct answer is: The figure is flipped across a line, producing a mirror image.
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