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Reflection and rotation are two of the most fundamental ideas in Non-Verbal Reasoning. Many CEM NVR questions ask you to identify reflected or rotated shapes, or to tell the difference between the two. Understanding these transformations deeply will help you across almost every NVR question type.
A reflection is a mirror image. Imagine placing a mirror along one edge of a shape — the image you see in the mirror is the reflection.
The shape is flipped over a vertical mirror line. Left and right are swapped, but top and bottom stay the same.
| Original | Reflected |
|---|---|
| Letter "b" | Letter "d" |
| Arrow pointing right (-->) | Arrow pointing left (<--) |
| Dot in top-left corner | Dot in top-right corner |
The shape is flipped over a horizontal mirror line. Top and bottom are swapped, but left and right stay the same.
| Original | Reflected |
|---|---|
| Letter "b" | Letter "p" |
| Arrow pointing up | Arrow pointing down |
| Dot in top-left corner | Dot in bottom-left corner |
A rotation is a turn around a central point. The shape spins but does not flip.
| Rotation | Description | Example |
|---|---|---|
| 90 degrees clockwise | A quarter turn to the right | Arrow up becomes arrow right |
| 90 degrees anticlockwise | A quarter turn to the left | Arrow up becomes arrow left |
| 180 degrees | A half turn | Arrow up becomes arrow down |
| 360 degrees | A full turn | Shape returns to its original position |
This is a crucial distinction in NVR:
| Transformation | What happens | Handedness |
|---|---|---|
| Rotation | The shape turns | Stays the same (a "right-handed" shape stays right-handed) |
| Reflection | The shape flips | Reverses (a "right-handed" shape becomes "left-handed") |
Think of it this way: if you write the letter "R" on a piece of paper, you can rotate the paper and the R will still look like an R (just turned). But if you reflect it (look at the back of the paper against a light), the R will be backwards.
A shape has:
After a horizontal reflection (left-right flip):
An L-shaped figure made of three squares arranged like this:
| Position | Description |
|---|---|
| Original | Two squares in a vertical column, one square attached to the right of the bottom square (like an "L") |
| 90 degrees clockwise | Two squares in a horizontal row, one square attached below the left square (like a rotated "L") |
| 180 degrees | Two squares in a vertical column, one square attached to the left of the top square (upside-down "L") |
Consider a flag shape: a vertical pole with a small triangular flag on the right side, pointing right.
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