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Difficulty: Medium2D Mental Rotation

A composite 2D figure is assembled from four disjoint polygon pieces. Before assembly, each piece must be mentally rotated clockwise from its starting orientation to a standard upright orientation.

- The Triangle's starting orientation is tilted 45° counter-clockwise from upright.
- The L-Shape's starting orientation is tilted 90° counter-clockwise from upright.
- The Trapezoid's starting orientation is completely inverted (180° from upright).
- The Rectangle's starting orientation is tilted 90° clockwise from upright.

Arrange the pieces in order from the SMALLEST clockwise rotation required to the LARGEST clockwise rotation required to align them for assembly.

  1. 1The Triangle
  2. 2The L-Shape
  3. 3The Trapezoid
  4. 4The Rectangle

Answer

The correct sequence from smallest to largest clockwise rotation is: Triangle (45°), L-Shape (90°), Trapezoid (180°), Rectangle (270°).
Based on a purely clockwise rotation requirement: the Triangle requires 45°, the L-Shape requires 90°, the Trapezoid requires 180°, and the Rectangle requires 270°. Ordering these degrees from smallest to largest results in Triangle, L-Shape, Trapezoid, Rectangle.

Step-by-Step Solution

1
Calculate the clockwise rotation for the Triangle.
The Triangle is tilted 45° counter-clockwise. Rotating it clockwise to the upright position requires 45°.
Moving clockwise from 45° left of vertical brings it to vertical.
2
Calculate the clockwise rotation for the L-Shape.
The L-Shape is tilted 90° counter-clockwise. Rotating it clockwise requires 90°.
Moving clockwise from 90° left of vertical brings it to vertical.
3
Calculate the clockwise rotation for the Trapezoid.
The Trapezoid is inverted (180°). Rotating it clockwise requires 180°.
180° is exactly halfway around.
4
Calculate the clockwise rotation for the Rectangle.
The Rectangle is tilted 90° clockwise. To reach the upright position moving only clockwise, it must complete the remaining 270°.
A full circle is 360°. Since it is already 90° clockwise, moving further clockwise to reach the top requires 360° - 90° = 270°.
5
Order the pieces based on rotation magnitude.
Triangle (45°), L-Shape (90°), Trapezoid (180°), Rectangle (270°).
Arranging from smallest to largest clockwise rotation as requested by the prompt.

Key Concept

Determining the magnitude of specific directional rotation (clockwise) to achieve a target spatial orientation.
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Topics

2D Mental Rotation

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