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

Concept

In a figure-series item built from a bent main stroke plus one attached branch, figures often pair up: the second figure of a pair is the reflection of the first about a vertical axis. Reflection is a rigid transformation — it flips every stroke's position and direction left-to-right, but it preserves each stroke's own topology: a branch that is a single unbranched curve stays a single unbranched curve, and a branch built from two strokes meeting at a point stays built from two strokes — only its position and orientation change.

Application

1. The first and second Problem Figures are one such pair: the second figure's hook-shaped bend and its branch both sit mirrored left-to-right from the first, and in both figures the branch is built from two short strokes meeting at a point — the same branching topology carried across the reflection.

2. The third Problem Figure introduces a different stroke family: a diagonal with a stepped zig-zag bend at the top-right (ending in a short tab pointing right), and — unlike the first pair's branch — a single, unbranched curling hook attached partway along the lower-left part of the stroke.

3. Reflecting the third Problem Figure for the missing fourth figure moves the zig-zag bend to the top-left with its tab pointing left, and moves the branch to the mirrored point on the right side of the stroke, preserving its single-unbranched-curve topology — reflection cannot turn one continuous stroke into two.

4. Only the figure labelled 2 among the Answer Figures shows exactly this: the zig-zag bend at the top-left with the tab pointing left, and a single unbranched curling hook attached partway along the stroke on the right.

Cross-check

The first pair confirms the topology rule: the second Problem Figure's bend and branch sit mirrored from the first, while the branch's own two-stroke construction carries over unchanged. The same rule requires the third Problem Figure's single, unbranched hook to stay unbranched after reflection — true only of the figure labelled 2.

Where the other figures go wrong

• Figures 1 and 3 among the Answer Figures attach the hook right at the stroke's lower end rather than as a branch off its body.

• Figure 4 forks the branch into two separate strokes — a topology reflection cannot produce from a single unbranched stroke.

• Figure 5 bends through a plain right angle at the top instead of the stepped zig-zag bend used by every Problem Figure.