Short Answer 
The process of transformation involves moving points in geometry and includes rotation, reflection, dilation, and translation. Rotation specifically preserves the shape and size of a figure, such as a trapezoid, while changing its orientation, illustrating the fundamental properties of geometric transformations.
Step 1: Understanding Transformation
Transformation is the process of moving a point from its original position to a new one. There are several types of transformations that are commonly studied, which include:
- Rotation – Turning a shape around a point.
- Reflection – Flipping the shape over a line.
- Dilation – Resizing the shape while maintaining proportions.
- Translation – Moving the shape in a straight line without changing its orientation.
Step 2: Exploring Rotation
In geometry, rotation is a specific type of rigid transformation that maintains the shape and size of the figure being rotated. When a point such as A(x, y) is rotated 180° around the origin, its new coordinate becomes A'(-x, -y). This means the point moves to a position directly opposite its original location.
Step 3: Applying Rotation to Trapezoid ABCD
The trapezoid ABCD, when rotated to form A’B’C’D, results in sides A’B’ being parallel to D’C’. This illustrates how rotation can affect the orientation of shapes while preserving their fundamental properties. Understanding this concept is essential when working with geometric transformations.