Reflection & Rotation

Two of the most important skills in Non-Verbal Reasoning are understanding reflection (flipping a shape) and rotation (turning a shape). Many NVR questions — including analogies, series, and matrices — rely on these transformations. This lesson will teach you exactly how each one works.

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What Is Reflection?

A reflection is what you see when you look in a mirror. The shape is flipped over a line (called the mirror line or line of reflection).

Horizontal Reflection (Left-Right Flip)

The shape is flipped as if there were a vertical mirror between the original and the reflection.

Original:       Reflected:
  F                 Ꟊ
                (backwards F)

Everything that was on the left moves to the right, and everything on the right moves to the left. But the shape does NOT flip upside down.

Vertical Reflection (Top-Bottom Flip)

The shape is flipped as if there were a horizontal mirror below it.

Original:       Reflected:
  ▲                 ▼
(triangle         (triangle
pointing up)     pointing down)

Everything that was at the top moves to the bottom, and vice versa. But left and right stay the same.

Key Rules for Reflection

Rule	Example
Left and right swap (horizontal reflection)	A shape pointing left now points right
Top and bottom swap (vertical reflection)	A shape pointing up now points down
The shape does NOT rotate	A reflected "L" looks like a backwards "L"
Size does not change	A reflected large shape is still large
Internal details are also reflected	A dot in the top-left moves to the top-right

How to Check a Reflection

1. Pick a distinctive feature (like a dot, a notch, or an arrow).
2. Check its position in the original.
3. In the reflection, that feature should be on the opposite side of the mirror line.

Example:

Original: A rectangle with a black dot in the top-left corner.
Horizontal reflection: The dot should be in the top-RIGHT corner.
Vertical reflection: The dot should be in the BOTTOM-left corner.

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What Is Rotation?

A rotation is when a shape is turned around a fixed point (usually its centre). Unlike reflection, rotation does not flip the shape — it spins it.

Common Rotation Amounts

Rotation	Description	Visual cue
90° clockwise	Quarter turn to the right	12 o'clock → 3 o'clock
180°	Half turn (upside down)	12 o'clock → 6 o'clock
90° anticlockwise	Quarter turn to the left	12 o'clock → 9 o'clock
270° clockwise	Three-quarter turn right	Same as 90° anticlockwise
360°	Full turn (back to the start)	12 o'clock → 12 o'clock

Visualising Rotation

Imagine pinning the shape to the page with a pin through its centre, then spinning it.

Example — rotating an "L" shape 90° clockwise:

Original:     90° CW:     180°:       90° ACW:
|             __|          __|            |
|                |            |           |
|__           __|                       __|

The "L" shape turns but never flips. This is the key difference from reflection.

How to Check a Rotation

1. Pick a distinctive part of the shape (e.g., the longest arm of an "L" or an arrow point).
2. Track where that part moves when you mentally turn the shape.
3. All parts of the shape move by the same amount in the same direction.

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Reflection vs Rotation: How to Tell the Difference

This is one of the most important skills for the exam. Sometimes a question asks: "Which option is a rotation of the shape?" and one of the wrong answers is a reflection (or vice versa).