| A | B |
|---|
| Transformations | change made to position or size of a figure |
| Image | Resulting figure after transformation is applied |
| Preimage | Original figure |
| Rotation | Turn |
| Reflection | Fip (mirror) of a figure over an imaginary line |
| Translation | Slide |
| How does a figure have symmetry? | If a figure and its image coincide (line up) |
| Translations | Transformation that slides each point of a figure the same distance in the same direction |
| Properties of Translations | Preserves congruence; preserves orientation; every point shifts "h" units horizontally and "k" units vertically |
| Using Reflections | Transformation in which each point of a figure has an image that is the same distance from the line of reflection as the original point. |
| Properties of reflections | Preserves congruence; changes (reverses) orientation; line of reflection is a perpendicular bisector of every segment that connects a point and its image |
| X-axis mapping | (a,b)->(a, -b) |
| Y-axis mapping | (a,b)->(-a, b) |
| Y=X | (a,b)->(b, a) |
| Y=-X | (a,b)->(-b, -a) |
| Rotation | Transformation in which every point moves along a circular path around a fixed point |
| Center of rotation | Fixed point |
| Angle of rotation | Segments drawn from a point and its image to the center of rotation always form the same angle |
| Properties of Rotations | Preserves congruence; preserves orientation |
| 90 degree rotation | (a,b)->(-b, a) |
| 180 degree rotation | (a,b)->(-a, -b) |
| 270 degree rotation | (a,b)->(b, -a) |
| 360 degree rotation | (a,b)->(a, b) |
| Glide Reflection | Translation followed by a reflection |
| Properties of Glide Relections | Preserves congruence; change (reverse) orientation; line of reflection is parallel to direction of translation |
| Dilations | Transformation that enlarges or reduces the original figure |
| Center of dilation | intersection of lines created by connecting corresponding vertices |
| Scale Factor (k) | Image length/original lenth |
| K>1 | Enlargement |
| 0<K<1 | Reduction |
| K=1 | No dilation (congruent figure) |
| Properties | Dilations do not preserve congruence (unless k=1); angle measures are preserved; dilations should be associated with similarity |
| Image length= | =K (original length) |
