Figure Analogies — Fundamental Concepts

Fundamental Concepts

Build a feature ledger

Compare the first pair under five headings: shape, position, orientation, shading and count. Mark what changes and what stays fixed. An object can move to a new cell without rotating, and it can rotate in place without changing its cell.

Apply the transformation

A clockwise quarter-turn sends up to right, right to down, down to left and left to up. With coordinates centred at the origin, it maps (x, y) to (y, −x). A vertical reflection instead maps (x, y) to (−x, y), and a horizontal reflection gives (x, −y). These rules help check a diagram when the shapes are described by positions.

Suppose the stated analogy rotates an outlined arrow clockwise and fills it. An outlined arrow initially pointing down should become a filled arrow pointing left. Keeping the outline misses one transformation; pointing right reverses the turn; copying the first example’s direction ignores the new input.

Check sufficiency

A symmetric unmarked figure may look unchanged under several transformations. One pair of counts may also fit both an additive and a multiplicative rule. Use additional examples or explicit wording to resolve those alternatives. If the information does not distinguish them, describe the ambiguity rather than manufacture a unique pattern.

Complete the solution by checking the whole result, including unchanged features. A candidate that gets rotation right but changes the number of elements still fails the analogy.