Question

Shown below is the perspective view of an object when viewed from the direction of the arrow. The object is first rotated by 90 degrees clockwise about the y-axis, then 180 degrees anti-clockwise about the x-axis, followed by 90 degrees anti-clockwise about the y-axis. All rotations are as viewed from a point on the positive axis towards the origin of the respective axes. Which option shows the CORRECT resultant view? 

• A. A
• B. B
• C. C
• D. D

Hint:

For 3D rotation problems, break the transformations down into steps, and apply each rotation in sequence to track the correct final orientation.

Answer 1

The Correct Option is C

Step 1: Visualize the rotations sequentially. The initial orientation is given, and the first rotation is 90 degrees clockwise about the y-axis.
Step 2: Next, apply the 180-degree anti-clockwise rotation about the x-axis.
Step 3: Lastly, rotate the object 90 degrees anti-clockwise about the y-axis. After performing these rotations, the object matches with.

Answer 2

The object is a round hub with four arm-like legs, one of which carries a taller upright wall that marks its orientation. Instead of imagining all three turns at once, it helps to track where that one marked leg points after each turn is applied in order: first 90 degrees clockwise about the vertical (Y) axis, then 180 degrees about the horizontal (X) axis, then 90 degrees anticlockwise about the vertical (Y) axis again.

1. Option A: The marked leg here ends up on the wrong side once the middle 180 degree flip about the X-axis is taken into account, so this does not match where the tracked leg lands after all three turns.
2. Option B: This view places the marked leg in a position that would only be reached by leaving out or mis-ordering one of the three turns, it does not follow from applying all three in the stated order.
3. Option C: Tracking the marked leg through all three turns in order, first the clockwise turn about Y, then the 180 degree flip about X, then the anticlockwise turn about Y, lands it exactly where this option shows it, with the hub the right way round for that combined motion.
4. Option D: This view has the marked leg's tall wall facing a direction that does not match the position reached after the full three-step turn, so it corresponds to a different (incorrect) combination of rotations.

Following the marked leg step by step through the clockwise Y turn, the X-axis flip, and the anticlockwise Y turn confirms it ends up exactly as shown in option C.

So the correct answer is Option C.