Transformations transformation One to One Mapping Preimage Point

Transformations

transformation • One to One Mapping Preimage Point Image Point A A´ • A change of position or size of a figure.

reflections • The mirror image of the original figure * The figures are congruent! * The original image is flipped!

Example: Line of Reflection

The line of Reflection is also called the line of symmetry.

It is also possible to have a reflection image with respect to a point.

Point of Symmetry • The point must be the midpoint for all segments that pass through it and have endpoints on the figure.

Example Does Rhombus MATH have point symmetry? Yes A M T H

translation • A transformation that moves points the same distance and in the same direction. * The figures are congruent! *Often referred to as a glide!

Example:

Translations are a composite of Reflections • One reflection over another with respect to two parallel lines. l m

rotation • A transformation that turns a figure about a fixed point. Fixed point Example:

Another Example:

Rotations are a composite of Reflections • One reflection over another with respect to two intersecting lines. l *Not drawn to scale! m

Center of rotation • The measure of the angle of rotation is twice the measure of the angle formed by the intersecting lines • Turn around Point

dilation • Alters the size of a geometric figure, but does not change its shape.

isometry • Congruence Transformation –Maps every segment to a congruent segment • No change in size! –Congruent sides and congruent angles

State whether each of the following have isometry. • Translation Yes • Reflection Yes • Rotation Yes • Dilation No