Spatial reasoning: distinguish a rotation from a reflection

What changes when a shape turns?

A rotation turns a shape around a point. A reflection flips it across a line. Both can move a marked corner, so one corner’s new position may not be enough to distinguish them.

Track at least two features and their order around the shape. For an asymmetric figure, reflection reverses that order, while rotation preserves it. Symmetric shapes may look identical after different transformations, so the task needs enough information.

Use a two-by-two arrangement

Original arrangement: A is at top left, B at top right, C at bottom left and D at bottom right. After a clockwise quarter-turn, the top row is C, A and the bottom row is D, B.

Reflect the original across a vertical centre line instead: the top row becomes B, A and the bottom row D, C. A reaches the same top-right position in both cases, but its neighbours reveal the difference.

Do not infer the whole move from one feature

If you look only at A, both transformations fit. Check B or C before accepting the answer. This is a useful example of why one supporting observation does not always establish a conclusion.

When reviewing a diagram, keep the starting orientation visible and name the turn precisely. “It moved right” does not distinguish a rotation from a reflection or a translation.

Trace before increasing the speed

Draw the four labelled cells, turn the paper or trace the movement by hand, then do the same task mentally. Use a new arrangement for the independent check.

Once you can explain the transformation, mix rotations and reflections in a short set. Review whether an error came from tracking, the direction of turn or confusing the two kinds of transformation.

Try it yourself

Start with top row A B and bottom row C D. What are the rows after a vertical reflection?