Question

which image shows the preimage reflected over the y - axis?
options: image b, none of these, image a, image c

Explanation:

To determine the reflection over the \( y \)-axis, we use the rule for reflecting a point \((x, y)\) over the \( y \)-axis: the image should be \((-x, y)\). This means the preimage and its reflection over the \( y \)-axis should be symmetric with respect to the \( y \)-axis (the \( y \)-axis is the perpendicular bisector of the segment joining a point and its image).

• For Image A: Visually, it does not show the preimage reflected over the \( y \)-axis (symmetry about \( y \)-axis is not present).
• For Image B: The preimage and Image B do not have the \( y \)-axis as the line of symmetry.
• For Image C: When we check the symmetry about the \( y \)-axis, the points of the preimage and Image C satisfy the reflection rule \((x, y) \to (-x, y)\) (they are symmetric with respect to the \( y \)-axis).

Answer:

Image C