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- Choose one distinctive corner or marked square and follow it through the transformation before moving the rest.
- Keep the operation precise: a clockwise turn and a mirror reflection are different. A reflection reverses handedness; a rotation does not.
- Check a second feature. The number of occupied squares and the distances between them should stay the same under a rigid movement.
1. Follow a marked square
Rotate this 3 × 3 board 90 degrees clockwise around its centre. Where does X land? Rows are numbered from top to bottom and columns from left to right.
Show answer and explanation: Follow a marked square
Row 1, column 3: the top-right corner.
The top-left corner travels to the top-right corner on a clockwise quarter-turn. On a three-by-three board, the row-column rule is (row, column) → (column, 4 − row). Applying it to (1, 1) gives (1, 3).
Check your method: A second clockwise quarter-turn would take X to the bottom-right, not back to its starting position.
2. Reflect, do not rotate
Reflect the marked square in the vertical mirror line through the middle column. Where does X land?
Show answer and explanation: Reflect, do not rotate
Row 2, column 3: the middle-right cell.
A vertical mirror swaps left and right while preserving the row. Column 1 becomes column 3; column 2 would stay on the mirror line. Do not move X up or down.
Check your method: Reflect the result again in the same line. It should return to row 2, column 1.
3. Rotate an entire shape
Rotate this board 90 degrees clockwise. List the three occupied cells in the rotated board.
Show answer and explanation: Rotate an entire shape
(1, 2), (1, 3), and (2, 2).
Apply the same rule to every cell: (1, 1) becomes (1, 3); (2, 1) becomes (1, 2); and the centre (2, 2) stays fixed. The rotated shape has two squares across the top, with one below the left of those two.
Check your method: There must still be exactly three squares. Rotating only the first square and guessing the rest can accidentally turn the L into its mirror image.
4. Follow a cube net
Fold this net into a cube without overlapping faces. Which letter is opposite C? Each letter represents one square face.
Show answer and explanation: Follow a cube net
E is opposite C.
Keep C as the base. A, B, D and F fold up to become its four neighbouring faces. E is attached to D, so it folds across the remaining opening, opposite the base. Faces sharing an edge with C cannot be opposite C.
Check your method: A is opposite F, and B is opposite D. There are three opposite pairs, using all six faces once.
5. Move without turning
A triangle has corners (1, 1), (1, 3) and (2, 1). Move every corner three units right and two units up on a standard x-y grid. What are the new corners?
Show answer and explanation: Move without turning
(4, 3), (4, 5), and (5, 3).
Moving right adds 3 to each x coordinate; moving up adds 2 to each y coordinate. Apply (+3, +2) consistently to all three points. Unlike a rotation, this translation does not change the direction of any side.
Check your method: The vertical side still has length 2 and the horizontal side still has length 1. Changing those lengths would distort the triangle.
6. Keep the order of operations
X starts in the top-left cell of a 3 × 3 board. First rotate the board 90 degrees clockwise, then reflect it across the vertical centre line. Where is X? Would reversing these operations give the same result?
Show answer and explanation: Keep the order of operations
X ends at the top-left. Reversing the operations puts it at the bottom-right.
In the stated order, the clockwise turn moves top-left to top-right, then the reflection moves it back left. In the reverse order, reflection moves top-left to top-right first; a clockwise turn then moves it to bottom-right. The operations do not commute.
Check your method: Write down the intermediate position after the first operation. Combining two instructions mentally without that checkpoint can hide an order error.
Turn an answer into a reusable method
After each question, write the step that made the solution clear. If you missed one, identify whether you misread the instruction, lost track of a position, or applied an inconsistent rule. Retry with that step visible. These six examples are not a calibrated test, and your total cannot establish an IQ, age ranking or population percentile.
Continue practising
- Pattern recognition practice
- Compare five reasoning categories with worked puzzles
- Prepare for a reasoning practice session
For a mixed session, try the free reasoning practice test. Read how its estimate works before interpreting the result.
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Answer key: Spatial reasoning
1. Follow a marked square
Row 1, column 3: the top-right corner. The top-left corner travels to the top-right corner on a clockwise quarter-turn. On a three-by-three board, the row-column rule is (row, column) → (column, 4 − row). Applying it to (1, 1) gives (1, 3).
Check: A second clockwise quarter-turn would take X to the bottom-right, not back to its starting position.
2. Reflect, do not rotate
Row 2, column 3: the middle-right cell. A vertical mirror swaps left and right while preserving the row. Column 1 becomes column 3; column 2 would stay on the mirror line. Do not move X up or down.
Check: Reflect the result again in the same line. It should return to row 2, column 1.
3. Rotate an entire shape
(1, 2), (1, 3), and (2, 2). Apply the same rule to every cell: (1, 1) becomes (1, 3); (2, 1) becomes (1, 2); and the centre (2, 2) stays fixed. The rotated shape has two squares across the top, with one below the left of those two.
Check: There must still be exactly three squares. Rotating only the first square and guessing the rest can accidentally turn the L into its mirror image.
4. Follow a cube net
E is opposite C. Keep C as the base. A, B, D and F fold up to become its four neighbouring faces. E is attached to D, so it folds across the remaining opening, opposite the base. Faces sharing an edge with C cannot be opposite C.
Check: A is opposite F, and B is opposite D. There are three opposite pairs, using all six faces once.
5. Move without turning
(4, 3), (4, 5), and (5, 3). Moving right adds 3 to each x coordinate; moving up adds 2 to each y coordinate. Apply (+3, +2) consistently to all three points. Unlike a rotation, this translation does not change the direction of any side.
Check: The vertical side still has length 2 and the horizontal side still has length 1. Changing those lengths would distort the triangle.
6. Keep the order of operations
X ends at the top-left. Reversing the operations puts it at the bottom-right. In the stated order, the clockwise turn moves top-left to top-right, then the reflection moves it back left. In the reverse order, reflection moves top-left to top-right first; a clockwise turn then moves it to bottom-right. The operations do not commute.
Check: Write down the intermediate position after the first operation. Combining two instructions mentally without that checkpoint can hide an order error.
Source: https://iqtestreal.com/practice/spatial-reasoning. Free non-clinical reasoning practice from IQTestReal.