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