Mirror Images — Fundamental Concepts

Fundamental Concepts

Apply a point rule to the whole figure

For a mirror at x = 0, the transformation is (x, y) → (-x, y). For a mirror at x = a, it is (x, y) → (2a - x, y). The second coordinate stays fixed; the first point and its image are equally far from the mirror.

Example: reflect (2, 7) across x = 5. The point is three units left of the mirror, so the image is three units right, at (8, 7). Negating x would use the wrong reference line.

Track two asymmetric features

A dot at the upper-left of a marked square moves to the upper-right under vertical reflection. A right-pointing arrow becomes left-pointing. Checking only one feature can admit an option that reflects the dot but rotates or preserves the arrow incorrectly.

Distinguish related operations

Vertical reflection preserves height.
A half-turn around the origin changes both coordinate signs.
Translation moves points without the reflection's equal-distance relationship to a line.
Reflecting twice across the same line restores the original.

The order of symbols in a horizontal row reverses, and each asymmetric symbol must itself be reflected. Simply reversing ordinary typed characters may not display the correct glyphs.

A symmetric border does not make the entire marked figure symmetric. Inspect its interior and position. A circle can preserve its shape while its centre changes location. The final candidate must satisfy the transformation for every relevant feature, not merely resemble the original in a different orientation.