Which option rotates the square 90 degrees (one quarter turn) clockwise?
The correct answer and explanation is:
iturn0image0turn0image1turn0image2turn0image3A 90-degree clockwise rotation, also known as a quarter-turn, transforms a square by repositioning its sides and any distinguishing marks. For instance, if a square has a unique feature, such as a dot on its top-left corner, rotating the square 90 degrees clockwise will move this dot to the top-right corner. This movement occurs because the top side of the square shifts to the right, the right side moves to the bottom, the bottom side moves to the left, and the left side moves to the top.
In the context of the provided image, the correct option is the one where the distinguishing mark (e.g., a black dot) has moved from its original position to the new position corresponding to a 90-degree clockwise rotation. For example, if the dot was initially at the top-left corner, after a 90-degree clockwise rotation, it should be at the top-right corner.
Understanding rotations is fundamental in geometry, as they are a type of transformation that preserves the shape and size of figures while altering their orientation. A 90-degree clockwise rotation specifically involves turning the figure one-quarter turn to the right around a fixed point, typically the center of the shape. This operation results in each point of the figure moving to a new position, maintaining the figure’s congruence.
To visualize this, consider a square with vertices labeled A, B, C, and D in a clockwise order. After a 90-degree clockwise rotation, vertex A moves to the position of B, B moves to C, C moves to D, and D moves to A. This systematic shift demonstrates how each point relocates during the rotation, effectively reorienting the square while preserving its dimensions and proportions.
In summary, identifying the correct option that represents a 90-degree clockwise rotation involves observing the new positions of the square’s sides and any unique features. By understanding the mechanics of rotational transformations, one can accurately determine how a figure like a square reorients after a specified rotation.
