Reasoning Chapter 04 : Figure Matrix | CET 12th 2026

Revision Notes — Figure Matrix

What is a Figure Matrix?

A Figure Matrix is a 2×2, 3×3, or 4×4 grid of geometric figures arranged in a logical sequence. One cell is left blank (marked "?"), and you must analyse the pattern row-wise and column-wise to find the figure that belongs there.

Core Analysis Rule

For a 3×3 grid, the relationship generally runs one of two ways:

• Row-wise: Figure 1 + Figure 2 → Figure 3, applied identically to Row 1, Row 2, and Row 3.
• Column-wise: Figure A + Figure B → Figure C, applied identically down each column.

Always test both directions before settling on a rule — most papers pick whichever direction is cleaner to spot.

The 16 Manipulation Types

Every figure-matrix question is built from one (or a mix) of these transformations:

Golden Priority Order

When a matrix looks like it could follow more than one rule, check in this order — the earliest rule that fits consistently across every row/column is almost always the intended one:

1. Rotation
2. Mirror / Flip
3. Addition / Deletion of elements
4. Movement of a component
5. Size or shape change
6. Shading change
7. Number pattern (counts of dots/lines)
8. Combination / Overlap (XOR)

If two options still look possible after applying the main rule, re-check shading and dot count last — that's usually where the difference is hidden.

Worked Example 1 — Rotation

If a figure turns by a fixed angle θ at every step, the angle of the n-th figure in a row is:

\( \theta_n = \theta_1 + (n-1)\times\theta \)

So for a 90° clockwise step starting at 0°, the sequence runs 0° → 90° → 180° → 270° → 360° ≡ 0°. A full 360° turn always returns the figure to its starting orientation.

Worked Example 2 — Number Pattern

When dots or lines increase by a constant step d per cell, the count in the n-th figure is:

\( D_n = D_1 + (n-1)\times d \)

For example, if Fig 1 has 2 dots and the step is +2, then Fig 2 has 4 dots and Fig 3 has 6 dots.

Worked Example 3 — Combination Rule

Two independent figures merge to form the third: a horizontal line plus a vertical line produces a plus sign. Symbolically, \( F_3 = F_1 \cup F_2 \). If instead the overlapping (shared) parts cancel out, that's the XOR variant: \( F_3 = F_1 \oplus F_2 \).

Exam Tips

• Scan the matrix row-wise first, then column-wise, then diagonally if neither works cleanly.
• Count elements (lines, dots, sides) before judging shape — miscounting is the most common mistake.
• When two answer options look identical at a glance, compare shading and dot count last, since that's where examiners usually hide the real difference.