1. transformations
Honors Geometry

2. Terms
Transformation – an operation that moves or changes a geometric figure in some way to produce a new figure.
Preimage – a figure before a transformation.
Image – a figure after a transformation.
Reflection – the flip of a figure about a line.
Translation – the slide of a figure.
Rotation – the movement of a figure about a fixed point.
Dilation – an enlargement or reduction of a figure.

3. More Terms
Congruence transformation – a transformation that preserves size and shape. Reflections, rotations and translations are congruence transformation.
Similarity transformation – a transformation that preserves shape but changes size. Dilations are similarity transformations.
Isometry – a synonym for congruence transformation.
Composition – two or more transformations that are combined to form a single transformation.
Glide reflection – a composition that combines a translation and a reflection.

4. Reflection
Reflect over the x-axis – Leave the x coordinate alone and change the sign of the y coordinate. (x,y)(x,y)
Reflect over the y-axis – Leave the y coordinate alone and change the sign of the x coordinate. (x,y)(x,y)

5. Translation
If translating a figure left or right, subtract or add to the x coordinate.
If translating a figure up or down, add or subtract to the y coordinate.
(x,y)(x+a,y+b)

6. Rotation
To rotate 90 counterclockwise – switch the x and y coordinates and change the sign of the new x coordinate
To rotate 90 clockwise (also known as 270 counterclockwise) – switch the x and y coordinates and change the sign of the new y coordinate.
To rotate 180 - change the signs of both the x and y coordinates.

7. Dilation
To enlarge a figure – multiply both the x and y coordinates by a scale factor greater than 1.
To reduce a figure – multiply both the x and y coordinates by a scale factor greater than zero and less than 1.

8. More Terms
Line symmetry – when a figure can be mapped onto itself over a line or lines.
Rotational symmetry – when a figure can be mapped onto itself by a rotation of 180 or less about the center of the figure.