# Honors Geometry Companion Book, Volume 1

1.2.3 Transformations in the Coordinate Plane (continued) Example 1 Identifying Transformations Reflections, translations, and rotations are three types of transformations where the position of the preimage is changed, but the size and shape of the preimage are not changed. In a reflection, the preimage is reflected, or flipped, over a line, called the line of reflection. You can think of the line of reflection as a mirror. When a figure is reflected, each point and its image are the same distance from the line of reflection. In a translation, the preimage is translated, or slid, such that all of the points on the preimage move the same distance in the same direction. In a rotation, the preimage is rotated, or turned, about a point, called the center of rotation. When a figure is rotated, each point and its image are the same distance from the center of rotation.

In the transformation shown here, the preimage is △ ABC and the image is △ A ′ B ′ C ′. Notice that if a mirror were placed between the two figures so that △ ABC was reflected in this mirror, the reflection in the mirror would be in the same position as △ A ′ B ′ C ′. Therefore, the transformation is a reflection and the line of reflection is a horizontal line between the two figures.

The transformation shown here may at first appear to be a reflection. However, notice that if a mirror were placed diagonally between the two figures, point Y would map to the position of point Z ′, not Y ′. If △ ABC is rotated 180° about the point P shown here, the result is △ A ′ B ′ C ′. Therefore, the transformation of △ ABC → △ A ′ B ′ C ′ is a rotation of 180°.

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