Honors Geometry Transformations Section 1 Reflections

A transformation is a movement of a figure in a plane from its original position to a new position.

The original figure is called the , while the figure resulting from the transformation is called the . A point in the image is usually named by adding a prime symbol (  ) to the name of the point in the preimage. preimage image

In a rigid transformation, or isometry, the image is congruent to the preimage.

We will consider three basic isometries: translations, reflections and rotations.

A reflection in a line m (or flip over line m) is a transformation that maps (or matches up) any point P to a point so that these two properties are true. 1. If P is not on m, then 2. If P is on m, then

Let’s take a look at reflections in the coordinate plane.

Example 1: Consider reflecting point A(3, 5) in the given line Example 1: Consider reflecting point A(3, 5) in the given line. Give the coordinate of its image. A   a) x-axis ________   b) y-axis ________   c) the line y = 1 _______   d) the line x = -2 ________

e) the line y = x _______   f) the line y=-x+2 _____   g) the line y = x - 1 _____

e) the line y = x _______   f) the line y=-x+2 _____   g) the line y = x - 1 _____

A figure has a line of symmetry if the figure can be mapped onto itself by a reflection in a line.

The previous statement is the formal definition of a line of symmetry, but it is much easier to think of a line of symmetry as the line where the figure can be folded and have the two halves match exactly.

Example 2: Draw all lines of symmetry.

Example 3: Name two capital letters that have exactly two lines of symmetry.