The set of reflections that would carry kite ABCD onto itself is: y-axis, x-axis, y-axis, x-axis.
What is Reflection?
A reflection, in geometry, is also referred to as a "flip". This is a type of transformation whereby a mirror image of an original image is created by reflecting it through a line of reflection. The new image created is congruent to the original image after reflection over a line.
For an image to be properly reflected, each point in the new figure must be equidistant from each of its corresponding points in the original figure.
Thus, given the image of kite ABCD below, to carry the kite onto itself, it means that each point in the new kite formed must be equidistant from each of the corresponding points in the original kite.
The second image attached below shows the set of reflections that would carry kite ABCD onto itself.
Therefore, the set of reflections that would carry kite ABCD onto itself is: y-axis, x-axis, y-axis, x-axis.
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