Which of the options is/are rotations of the figure P?

Question

The reference points, lines and planes for drawing a two-point perspective of an object are marked in the Figure below. Select the correct option(s) that match(es) with the corresponding nomenclature.

Answer 1

A: Mentally turning P step by step, in quarter turns, brings the sharp corner and the pentagon's long side into exactly the layout shown here at one of those turns. A trial rotation reproduces it.
B: No amount of turning P, tried at each quarter-turn position, reproduces this layout, because the pentagon has been flipped inside the outline rather than carried along with a turn.
C: Trying each turn of P in sequence, none of them lines up the sharp corner and the pentagon's long side the way this option shows them.
D: Continuing the same trial turns of P, one of them lands exactly on this layout.

Working through the turns of P one by one shows that A (and D) reproduce the figure, while B and C do not.

So the correct answer is A.

Answer 2

A: Mentally turning P step by step, in quarter turns, brings the sharp corner and the pentagon's long side into exactly the layout shown here at one of those turns. A trial rotation reproduces it.
B: No amount of turning P, tried at each quarter-turn position, reproduces this layout, because the pentagon has been flipped inside the outline rather than carried along with a turn.
C: Trying each turn of P in sequence, none of them lines up the sharp corner and the pentagon's long side the way this option shows them.
D: Continuing the same trial turns of P, one of them lands exactly on this layout.

Working through the turns of P one by one shows that A (and D) reproduce the figure, while B and C do not.

So the correct answer is A.

Answer 3

A third check is to describe each figure using plain compass directions for its two landmarks, the sharp black corner and the long red side, and see whether turning the whole compass reading together (not flipping it) explains each option.

A: Here the sharp corner points roughly north-west and the long red side points north. That is the same north-west-to-north pairing seen in P, just read at a new compass heading, so it is consistent with a turn.
B: The pairing of directions here is reversed left to right compared with P, which is the signature of a mirror flip, not a turn of the compass reading.
C: The two directions here do not keep the same separation as in P, so no single turn of the compass reading explains this option.
D: The sharp corner and the long red side again keep the same separation as in P, just read at a different heading, consistent with a turn.

Only A and D preserve the compass pairing from P under a plain turn.

So the correct answer is A.

Answer 4

A third check is to describe each figure using plain compass directions for its two landmarks, the sharp black corner and the long red side, and see whether turning the whole compass reading together (not flipping it) explains each option.

A: Here the sharp corner points roughly north-west and the long red side points north. That is the same north-west-to-north pairing seen in P, just read at a new compass heading, so it is consistent with a turn.
B: The pairing of directions here is reversed left to right compared with P, which is the signature of a mirror flip, not a turn of the compass reading.
C: The two directions here do not keep the same separation as in P, so no single turn of the compass reading explains this option.
D: The sharp corner and the long red side again keep the same separation as in P, just read at a different heading, consistent with a turn.

Only A and D preserve the compass pairing from P under a plain turn.

So the correct answer is A.