1. TRANSFORMATIONS Objective:  To identify isometries  To find reflection images of figures

2. Translation RotationDilation A reflection produces a mirror image of a figure along a line of reflection. A translation moves every point on a figure the same distance in the same direction. A rotation turns a shape about a fixed point. To perform a rotation, three details are needed: 1) The center 2) The angle of rotation and 3) The direction of rotation A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape.

3. IMPORTANT TERMS Isometry - A transformation that does not change the shape or size of a figure. In other words, it preserves lengths, angle measures, parallel lines, and distance between points. Pre-image - the figure prior to the transformation Image – the figure after the translation

4. TRANSLATIONS-SLIDE! To translate a shape every point must move:  the same distance  In the same direction

5. EXAMPLE #1

6. ROTATIONS-TURN!  "Rotation" means turning around a center.  The distance from the center to any point on the shape stays the same  Go counter-clockwise COUNTER CLOCKWISE PREIMAGE [Before] IMAGE [After]

7. EXAMPLE #2

8. REFLECTIONS-FLIP! A reflection is a transformation in which the figure is the mirror image of the other. Notice that in each case, the pre-image is always the same distance away from the line of reflection as the image. Very important!

9. LINES OF SYMMETRY

10. EXAMPLE #3

11. DILATIONS-GROW OR SHRINK! A dilation enlarges or reduces the size of a shape; this is why the pre-image and image of a dilation are not congruent, but similar. Every dilation has a center point and a scale factor.

12. EXAMPLE #4