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Question

Difficulty: Medium2D Mental Rotation

An asymmetric L-shaped bracket has its long arm pointing North and its short arm pointing West. The long arm features a semi-circular notch on its East-facing edge. To assemble a complex mechanism, this bracket must be mentally rotated clockwise to fit into various component slots. Arrange the following orientations of the bracket in order of the clockwise angular shift required to reach them from the initial position, starting from the smallest clockwise rotation and ending with the largest.

  1. 1Long arm points East, short arm points North, with the notch facing South
  2. 2Long arm points South-East, short arm points North-East, with the notch facing South-West
  3. 3Long arm points South-West, short arm points South-East, with the notch facing North-West
  4. 4Long arm points West, short arm points South, with the notch facing North

Answer

The correct sequence of orientations based on their required clockwise rotation is: 90° (East-pointing long arm), 135° (South-East-pointing long arm), 225° (South-West-pointing long arm), and 270° (West-pointing long arm).
By tracking the long arm of the bracket, we can determine the exact angular shift. The initial position is North (0°). The required clockwise rotations are 90° (to East), 135° (to South-East), 225° (to South-West), and 270° (to West). Placing them in ascending order yields this exact sequence.

Step-by-Step Solution

1
Analyze the initial reference orientation of the bracket.
The long arm is at 0° (North), the short arm is at 270° (West), and the notch is at 90° (East).
Establishing a baseline is necessary to calculate the angular shifts.
2
Calculate the rotation required for the orientation with the long arm pointing East.
Moving from North (0°) to East (90°) is a 90° clockwise rotation.
This determines the angular shift for the first described orientation.
3
Calculate the rotation required for the orientation with the long arm pointing South-East.
Moving from North (0°) to South-East (135°) is a 135° clockwise rotation.
This determines the angular shift for the second described orientation.
4
Calculate the rotation required for the orientation with the long arm pointing South-West.
Moving from North (0°) to South-West (225°) is a 225° clockwise rotation.
This determines the angular shift for the third described orientation.
5
Calculate the rotation required for the orientation with the long arm pointing West.
Moving from North (0°) to West (270°) is a 270° clockwise rotation.
This determines the angular shift for the fourth described orientation.
6
Arrange the determined angular shifts in ascending order.
The order is 90°, 135°, 225°, then 270°.
The question requests the order from the smallest to the largest clockwise rotation.

Key Concept

2D Mental Rotation
Estimated Time:1m 30s
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Topics

2D Mental Rotation

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