Select a suitable figure from the Answer Figures that would replace the…

Concept

In a figure-series problem, each step applies the SAME geometric transformation to the previous figure. A transformation can be a composition of two independent operations: a ROTATION (turning the figure about its centre by a fixed angle) followed by a REFLECTION (flipping it across an axis). A 90 degree anticlockwise (ACW) rotation moves a point that was pointing up so it now points left; a vertical inversion then flips the result top-to-bottom (a mirror image across a horizontal axis). The two operations are applied in order, so you must rotate first and then flip.

Applying the rule to this series

The governing rule for this series is: each figure is rotated 90 degrees anticlockwise and is then vertically inverted (flipped top-to-bottom). Trace the last given figure through these two steps:

1. Start with the given curl figure (the spiral whose open hook points towards the upper side).

2. Rotate it 90 degrees anticlockwise: the hook that pointed up now swings round to point to the left, and the body of the spiral turns onto its side, becoming a broad, mostly horizontal curl.

3. Vertically invert that rotated figure (flip it top-to-bottom): the now-horizontal curl is mirrored across a horizontal line, so the open mouth of the spiral and its trailing hook settle into their final position, giving the wide spiral whose loop opens to the left with the small hook trailing to the right.

The figure produced by rotating 90 degrees anticlockwise and then inverting vertically is the wide left-opening spiral with the trailing hook on the right — this matches Answer Figure 3.

Why the other answer figures do not fit

• The two figures whose hook turns upward keep the spiral standing in an orientation that a 90 degree ACW turn cannot produce — the rotation must lay the curl onto its side, not leave it upright.

• The figure that is squashed into a flat oval changes the proportions of the curl; rotation and reflection are rigid motions and never stretch or compress the figure, so its shape must be preserved.

• The remaining figure has its loop and hook curling in the wrong sense — it corresponds to a clockwise turn or to a horizontal (left-right) flip rather than the required anticlockwise turn followed by a top-to-bottom flip.

Rule (reference figure)