Reflect across the Vertical Axis

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Reflect (2,−3) across the y-axis. Candidate answers: (A) (2,3) (B) (−2,3) (C) (−2,−3) (D) (−3,2).
• Independent check inputs: Reflect (3,−4) across the y-axis. Candidate answers: (A) (3,4) (B) (−3,4) (C) (−3,−4) (D) (−4,3).

Learn the idea

Translations, reflections and rotations preserve distances and angle measures. Coordinate rules describe these moves exactly, and a sequence of moves must be applied in its stated order to determine the final image. Reflection across the y-axis negates a point’s horizontal coordinate and leaves its vertical coordinate unchanged. The original and image lie equally far from the mirror line on opposite sides.

Here is the method on the supplied teaching case. A y-axis reflection negates x and keeps y. Points stay the same horizontal distance from the y-axis on the opposite side.

Negate x for a y-axis reflection, even though the axis name contains y. Points already on that axis remain fixed; a reflection generally reverses orientation while preserving length.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Reflect (9,−10) across the y-axis. Candidate answers: (A) (9,10) (B) (−10,9) (C) (−9,10) (D) (−9,−10). Show the mathematical reason, not only the selected answer. Expected result: (−9,−10). A y-axis reflection negates x and keeps y. Points stay the same horizontal distance from the y-axis on the opposite side.

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