6.2 Mirror Images

6.2 Mirror Images

Quick Answer: A mirror flips left and right only. Draw a vertical axis through the centre of the figure and reflect every feature across it. Do not confuse a mirror image (left-right flip) with a water image (top-bottom flip). Symmetric figures look the same after mirroring, so always check whether the figure has a vertical symmetry axis before you commit to an answer.

A mirror image is what you see when a figure is reflected in a plane mirror placed vertically to the page. The mirror reverses the component of the figure that is perpendicular to the mirror plane. For a vertical mirror, that component is left-right, so the image is laterally inverted.

Why Left-Right and Not Up-Down?

A vertical mirror reverses the axis perpendicular to its surface — the horizontal axis. The vertical axis lies parallel to the mirror, so it is preserved. This is a geometric fact, not a biological quirk: a horizontal mirror (placed flat, like the surface of still water) reverses the vertical axis instead, producing a water image.

The Reflection Method

1. Draw the mirror axis — a vertical line through the centre of the figure (or along the stated mirror line if the axis is offset).
2. Identify features — corners, dots, open ends, asymmetric strokes.
3. For each feature, measure its horizontal distance to the axis. Place the mirror image of the feature on the opposite side at the same distance.
4. Preserve vertical position — a feature at the top stays at the top; a feature at the bottom stays at the bottom.
5. Reverse handedness — if a stroke opens to the right, its mirror opens to the left.

Worked Example 1 — The Letter P

The letter P has a vertical stem on the left and a bowl that opens to the right. Mirror it across a vertical axis through its centre:

• The stem moves to the right side.
• The bowl now opens to the left.
• The result reads as a backwards P — a mirrored P that faces the opposite way.

Worked Example 2 — The Digit 3

The digit 3 is made of two bowls, both opening to the left. Mirror it:

• Both bowls now open to the right.
• The result looks like the digit E without the vertical bar, or a backwards 3.

Worked Example 3 — A Compass Arrow

A compass arrow points north-east (toward 1:30 on the clock). Mirror it across a vertical axis:

• The north component stays north (up is preserved).
• The east component becomes west.
• The arrow now points north-west (toward 10:30).

Note carefully: a 90° CW rotation of the same arrow would send it to 4:30 (south-east). A mirror image is NOT a rotation. They produce different results whenever the figure is asymmetric.

A Mermaid Diagram of Mirror Reflection

The diagram shows a feature at horizontal distance d to the left of a vertical mirror axis. Its mirror image appears at distance d to the right of the axis.

Mirror vs Water — A Critical Distinction

The PAF exam sometimes uses water images as distractors inside a mirror-image set. A water image is what you see when a figure is reflected in a horizontal mirror (like the surface of a pond). It flips the figure top-to-bottom while preserving left-right.

If a question says "mirror image" and an answer choice shows the figure flipped top-to-bottom, that is a water image — eliminate it.

Common Traps

Trap 1 — Symmetric Figures

A figure with a vertical symmetry axis looks identical to its mirror image. The letter O, the digit 8, a circle, a square oriented with edges vertical/horizontal, and the letter A all have vertical symmetry. If a figure is symmetric, the correct mirror image is the figure itself — do not invent a flip that is not there.

Trap 2 — Treating Mirror as Rotation

A mirror image and a 180° rotation are different transforms. The mirror reverses handedness; the 180° rotation preserves it. For the letter R:

• Mirror: backwards R.
• 180° rotation: upside-down R (still readable as R).

These are different answers. Read the question stem carefully — "mirror image" and "rotated 180°" are not interchangeable.

Trap 3 — Offset Mirror Axis

Some items place the mirror axis to one side of the figure rather than through its centre. The reflection still preserves distance to the axis, but the mirror image will sit on the opposite side of the axis at the same distance. Do not assume the axis is always central.

A Chart of Letter/Digit Mirror Difficulty

The chart below ranks common items by how often candidates miss them. Highly asymmetric letters are easiest; symmetric ones cause the most errors because candidates over-flip them.

Speed Strategy

• Scan for vertical symmetry first. If the figure has a vertical symmetry axis, the mirror image is the figure itself. Pick that option and move on.
• For letters, mentally swap left and right strokes. The stem of P, the cross-bar of A, the tail of R — each swap gives you the mirror in under a second.
• For arrows, only the horizontal component of the direction flips. North stays north; east becomes west. South stays south; west becomes east.
• Eliminate water images the moment you see them in a mirror-image question — they are a guaranteed wrong answer.

Practice Drills

1. Write the alphabet in capitals. For each letter, mark whether it has vertical symmetry, horizontal symmetry, both, or neither. Mirror each letter mentally and check by holding it up to a real mirror.
2. Look at a clock face in a mirror. The numbers appear reversed left-to-right, but 12 stays at the top and 6 stays at the bottom. Read the mirror time and check against the real time.
3. Hold a page of text up to a mirror. Notice that left and right swap but the lines of text still read top-to-bottom. This is lateral inversion in action.

The next section moves from single-figure transforms to matrix reasoning, where you must derive rules across rows and columns of figures.