Question

answer
a reflection over the x -axis
a reflection over the y -axis
a rotation 180° counterclockwise about the origin
a rotation 90° counterclockwise about the origin
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Explanation:

To determine the transformation for Figure E (assuming context of coordinate - plane transformations):

• Reflection over x - axis: Changes \((x,y)\) to \((x, - y)\).
• Reflection over y - axis: Changes \((x,y)\) to \((-x,y)\).
• 180° rotation (counter - clockwise about origin): Changes \((x,y)\) to \((-x, - y)\).
• 90° rotation (counter - clockwise about origin): Changes \((x,y)\) to \((-y,x)\).

If Figure E is on one side of the y - axis and its image (after transformation) is on the other side, a reflection over the y - axis (which flips the figure across the y - axis) is a common transformation. For example, if a point \((2,3)\) is on Figure E, after reflection over y - axis, it becomes \((-2,3)\), which is a flip across the y - axis.

Answer:

A reflection over the \(y\) - axis