Transformations

half turn

180 degrees

three-quarters turn

270 degrees

full-circle turn

360 degrees

90 degree turn

90 degrees

preimage

A figure before a transformation is applied. The original figure.

Rotational symmetry

A figure can be rotated less than 360 degrees around a central point and coincide with the original figure.

Line of reflection

A line that a figure is flipped across to create a mirror image of the original figure

Axis of symmetry

A line that divides a plane figure or a graph into two congruent reflected halves

Isometry

A transformation that does not change the side or shape of the figure being transformed. (The direction it faces may be changed though.) << translations, reflections, & rotations >>

Basic Rigid Motion

A transformation that preserves side lengths and angle measures. Direction isn't preserved << translations, reflections, & dilations >> Also called an isometry.

Composite Transformation

A transformation that results from two or more transformations. The image of one transformation is the pre-image of the next transformation.

translation

A transformation that shifts or slides every point of a figure or graph the same distance in the same direction. (slide)

Prime Notation

After a transformation, corresponding points are labeled using _____________________

Dilation Notation

Dilations are represented by a capital D.

Direct isometry

Distance is preserved (the same). direction is preserved (the same).

Reflection Notation

Reflections are a lower case r.

Rotation of -180 degrees

Rotate the graph 180 degrees clockwise

Definition - Rotation of 180 degrees

Rotate the graph 180 degrees counter-clockwise. Note - rotating a graph 180 degrees clockwise happens to be the same thing

Definition - Rotation of -270 degrees

Rotate the graph 270 degrees clockwise

Definition - Rotation of 270 degrees

Rotate the graph 270 degrees counter-clockwise

Definition - Rotation of -90 degrees

Rotate the graph 90 degrees clockwise

Definition - Rotation of 90 degrees

Rotate the graph 90 degrees counter-clockwise

Rotation Notation

Rotations are a capital R.

Image

The figure you get after a transformation is applied.

Rotation

The transformation of a figure that is around a fixed point. (turn)

Definition - Reflection

The transformation of a figure that is over a line (flip).

Translation Notation

Translations are a capital T.

Line of symmetry

a line that divides a figure into two halves that are mirror images of each other

Definition - Dilation

a transformation that enlarges or reduces the original figure proportionally by multipling both coordinates by the scale factor. (enlarge or reduce)

Rule - Reflection over the y axis

change the sign of the x coordinate.

Rule - Reflection over the x axis

change the sign of the y coordinate.

counterclockwise

in the direction that is opposite of the direction the hands on the clock move

clockwise

in the same direction as the rotating hands of a clock

Rule - Reflection over y=-x

switch the x and y coordinates and negate them.

Rule - Reflection over the line y=x

switch the x and y coordinates.

Angle of rotation

the angle through which a preimage is rotated to form the image; the number of degrees a figure is rotated

order of symmetry

the number of times a figure maps onto itself as it rotates