Transformation Sequences

Identifying the next shape in a series of progressive transformations.

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Identifying the next shape in a series of progressive transformations.

Transformation sequences involve shapes that undergo progressive changes following a consistent pattern. Each step applies the same transformation (rotation, scaling, or mirroring) to produce the next shape. The challenge is to identify the transformation rule and predict what comes next.

shape[n+1] = transform(shape[n], rule)

Each shape rotates 45° clockwise from the previous
Shape alternates between mirrored and unmirrored states
Combined rotation and color change at each step

How to recognize it

Compare adjacent shapes to find the transformation
Verify the same transformation applies at each step
Apply the transformation to the last shape to predict next
Check for compound transformations (rotation + other change)

Common mistakes

Assuming simple rotation when compound transformation applies
Missing alternating patterns in the sequence
Not verifying the rule works for all consecutive pairs

Step-by-step walkthrough

A sequence shows a triangle pointing up, then right, then down. What is the next shape in the sequence?

Compare the first two shapes: triangle rotates from pointing up to pointing right.
Calculate the rotation: up to right is 90 degrees clockwise.
Verify with the next pair: right to down is also 90 degrees clockwise.
Apply the same transformation to the last shape: down rotated 90 degrees clockwise.
Down rotated 90 degrees clockwise points to the left.

Answer: A triangle pointing left

Practice guidance

Spatial Reasoning