Final answer:
Dilations affect the size of angles, circles, and line segments without changing their shape. Translations preserve angles, circles, perpendicular lines, parallel lines, and line segments. Reflections create mirror images of figures, reversing the orientation of angles and line segments. Rotations turn figures around a fixed point, preserving angles, circles, perpendicular lines, parallel lines, and line segments.
Step-by-step explanation:
It requires a comparison between different geometric transformations, specifically dilations, translations, reflections, and rotations, with a focus on their effects on various geometrical concepts such as angles, circles, perpendicular lines, parallel lines, and line segments. When making such comparisons, we explore how these transformations alter or maintain the properties of geometrical figures. A translation moves every point of a figure or a space by the same distance in a given direction. Parallel lines remain parallel, the lengths of line segments remain unchanged, and angles remain the same size, preserving the overall shape and size of the figure. Dilations, on the other hand, are transformations that produce a figure similar to the original by proportionally enlarging or reducing it. In dilations, angles remain unchanged, but the distances between points are scaled by a common factor. Circles under dilation will remain circles but with a different radius. A reflection is a transformation producing a mirror image of a figure across a line of reflection. It preserves the size and shape of the figure, the lengths of line segments, and mirror image angles while flipping the orientation of the figure. Rotations turn a figure about a fixed point, known as the center of rotation, through a specified angle and direction. The distances from the center of rotation to any point on the figure and the angle size remain constant, maintaining the overall shape and size of the figure.