Question

Which of the following bescribes a geometrie rotation?Wransformation that turns a figure around a point anlamation that slides a figure to a new locationAwastoration that is a ligure across a line D transformation that enlarges or reduces the size of a figure by certain scale factor

Answer 1

A geometric rotation is a type of transformation that involves rotating a figure around a fixed point called the center of rotation.

Step-by-step explanation:

This rotation preserves the shape and size of the figure, only changing its orientation. The description "transformation that turns a figure around a point" accurately characterizes a geometric rotation. During a rotation, each point in the figure moves along a circular path, and the distance of each point from the center of rotation remains constant.

To elaborate, consider a figure with points (x, y) and its rotation by an angle θ around the origin (0, 0). The coordinates of the rotated point (x', y') can be expressed using the rotation formulas:
`\[x' = x \cdot \cos(\theta) - y \cdot \sin(\theta)\]`
`\[y' = x \cdot \sin(\theta) + y \cdot \cos(\theta)\]`. These formulas ensure that the figure undergoes a smooth rotation without changing its size.

In summary, a geometric rotation involves turning a figure around a fixed point, and during this transformation, the figure maintains its shape and size, only changing its orientation. The rotational behavior is crucial for various applications in geometry and computer graphics.