Which option rotates the square 90 degrees (one quarter turn) clockwise?
The correct answer and explanation is :
To determine which option rotates a square 90 degrees clockwise, we need to understand the effect of such a rotation on the square’s orientation.
Understanding 90-Degree Clockwise Rotation:
Consider a square with vertices labeled A, B, C, and D, starting from the top-left corner and proceeding clockwise. A 90-degree clockwise rotation around the center of the square transforms each vertex as follows:
- Vertex A (top-left) moves to the top-right position.
- Vertex B (top-right) moves to the bottom-right position.
- Vertex C (bottom-right) moves to the bottom-left position.
- Vertex D (bottom-left) moves to the top-left position.
This transformation shifts the entire square’s orientation by one-quarter turn in the clockwise direction.
Applying the Rotation:
To visualize this, imagine the square placed on a coordinate plane with its center at the origin (0,0). Initially, the vertices might be at positions such as (-1, 1), (1, 1), (1, -1), and (-1, -1). A 90-degree clockwise rotation would reposition these vertices to (1, 1), (1, -1), (-1, -1), and (-1, 1), respectively.
Identifying the Correct Option:
Without access to the specific image provided in the link, we can deduce that the correct option is the one where the square’s vertices have moved according to the transformation described above. Typically, this would be the option where:
- The vertex that was initially at the top-left corner (A) is now at the top-right corner.
- The vertex that was initially at the top-right corner (B) is now at the bottom-right corner.
- The vertex that was initially at the bottom-right corner (C) is now at the bottom-left corner.
- The vertex that was initially at the bottom-left corner (D) is now at the top-left corner.
Conclusion:
In the absence of the actual image, the option that shows the square with its vertices repositioned as described above represents the square rotated 90 degrees clockwise. This transformation is fundamental in geometry and is widely used in various applications, including computer graphics and spatial reasoning.