Transformations: Rorations Flashcards
Pre-image
A figure that is about undergo a transformation
Transformation
A function that moves something along a coordinate plane
Image
A figure that has undergone my transformation
Distance Preserving
The distance between the image of the two points is always equal to the distance between the pre-image of the two points
Angle preserving
The angle measure of the image is equal to the angle measure of the pre-image
What do you need to perform a rigid motion rotation?
The center of rotation and direction
Rotational Symmetry
If a figure is it’s own image under a center of rotation and the center of the rotation is the only fixed point
Order of Rotational Symmetry
The number of degrees a figure must be rotated in order to see an identical image
Positive rotations
Counter-clockwise
Negative Rotations
Clockwise
How do u name the equivalent rotation?
Subtract the # by 360
Rotation of 180 degrees
P(x,y)–p’(-x,-y)
Rotation of 90 degrees
P(x,y)–p’(-y,x)
Rotation of -90 degrees
P(x,y)–p’(y,-x)
Rotation of 360 degrees
P(x,y)–p’(x,y) (orientation is maintained)
Rotation of 270 degrees
P(x,y)–p’(y,-x)
After a rotation, point P= P’
Point P and point P’ were two distinct points located on the same arc of rotation
Point P and point P’ were two distinct points equidistant from the center of rotation
Rotation over the y axis (ry-axis)
P(x,y)–P’(-x,y)
Rotation over the x axis (rx-axis)
P(x,y)–P’(x,-y)
Reflection over the line y=x
P(x,y)–P’(y,x)
Reflection in the line y=-x
P(x,y)–P’(-y,-x)
Basic Rigid Motion (Isometry)
A transformation that preserves lengths of two segments and measures of angles
Rigid motion
Performing a transformation that didn’t change the size/ angle measure
R o=
R 180
Name the order of rotational symmetry for regular polygons
360/N (# of sides)
Point symmetry
180 degrees
State the properties in which dilation
is altered
K1 ~ get larger
Which is not an Isometry? Line reflection Dilation Point reflection Translation
Dilation
Which property isn't preserved under ry=x? Distance Angle measure Orientation Parallelism
Orientation
Which transformation is a direct Isometry?
(x,y)-(-x,-y)
And
(x,y)-(x-5,y-2)
Which transformation does not preserve orientation? (x,y)-(-x,-y) (x,y)-(x+3,y+2) (x,y)-(2x,2y) (x,y)-(y,x)
(x,y)-(y,x)
Which transformation is an example of a direct Isometry? rx, R40, D-3, ry=5
R40
Which transformation is an opposite Isometry? R-90 T3,-4 D-2 rx=1
rx=1
If KL=8 and K’L’=12, then the constant of dilation is ___ an the dilation is a (an) ____
12/8=3/2
3/2, enlargement
Point reflections preserve
Distance, angle measure, and orientation
Find the image under the same dilation
K= ending/beginning
Find 3 transformations with the same output
R0, R180, D-1
-x,-y
Opposite isometries
Line reflections and glide reflections
Direct isometries
Point reflections, rotations, and translations
Preserve orientation
Composition
The output of one transformation is the input of another transformation. Work from right to left
Dilation
Increasing size, perimeter changes, orientation is invariant
Find D2 ° D1/2 of (x,y)
Inverse (x,y) - (x,y)
It stays the same
If line a is parallel to line b, then ra ° rb (^ CTH) is equivalent to a
Translation
ry=x ° rx produces a transformation that is
A direct Isometry
When u dilate a pre-image the image’s angles are in a
1:1 ratio
What transformation doesn't preserve orientation? (x,y)-(-y,x) (x,y)-(-y,-x) (x,y)-(y+3,x) (x,y)-(-3y,-3x)
(x,y)-(-y,-x)
