Unit 6: Transformations (Ch 9) Flashcards
transformation
A transformation moves or changes a figure to produce a new figure.
preimage
The original figure is called the preimage.
image
The new figure is called the image.
transformation statement
A transformation statement describes the “mapping” of each preimage point to its image point. EX: ABC ==> A’B’C’
(Explains how the preimage points will move to the image points.)
prime notation
Use prime notation to name an image. EX: ABC ==> A’B’C’
This labels the image so that it is not confused with the preimage. It is an apostrophe
reFLection
FLip - a mirror image of the original figure.
tranSLation
SLide - moves every point of a figure the same distance in the same direction.
roTation
Turn - a figure is turned about a fixed point.
diLationS
Larger or Smaller - a figure is enlarged or reduced.
congruence transformation
Changes the position of the figure without changing its size or shape.
isometry
Another word for “congruence statement.” Changes the position of the figure without changing its size or shape.
All transformations are isometries, EXCEPT dilations!
reflection
A reflection uses a line of reflection to create a mirror image of the original image.
REFLECTION
In reflection, what two things are the same distance from the line of reflection?
In reflection, each point of the preimage and its corresponding point in the image are the same distance from the line of reflection.
REFLECTION
What information do we know if the point is on the line of reflection?
If the point is on the line of reflection, then the image and preimage are the same point.
REFLECTION
What information do we know if the point does NOT lie on the line of reflection?
If the point does NOT lie on the line of reflection, the line of reflection is the perpendicular bisector of the segment joining the two points.
REFLECTION COORDINATE RULES
Reflecting over the x - axis
(x, y) ==> (x, -y)
Change the sign of the y coordinate.
REFLECTION COORDINATE RULES
Reflecting over the y - axis
(x, y) ==> (-x, y)
Change the sign of the x coordinate.
REFLECTION COORDINATE RULES
Reflecting over the line y = x
(x, y) ==> (y, x)
Swap the x and y coordinates.
REFLECTION COORDINATE RULES
Reflecting over the line y = -x
(x, y) ==> (-y, -x)
Swap the x and y coordinates and change the sign of both of the new x and y coordinates.
translation
A translation moves every point of a figure the same distance in the same direction.
TRANSLATION
coordinate notation for a translation
(x, y) ==> (x+a, y+b) Each point (x, y) is translated horizontally "a" number of units and vertically "b" number of units.
TRANSLATION
vector notation for a translation
<a>
This tells us how many units each point will slide.
“a” tells us what direction the x coordinates will move and “b” will tell us what direction the y coordinates will move.</a>
rotation
A rotation turns a figure about a fixed point called the center of rotation.
ROTATION
Which direction is a rotation understood to move?
Rotations are counterclockwise (CCW), unless stated to be clockwise (CW).
ROTATION
Coordinate rules for rotations about the origin (CCW)
For a rotation of 90°
(x, y) ==> (-y, x)
Swap the x and y coordinates and chance the sign of the new x coordinate.
ROTATION
Coordinate rules for rotations about the origin (CCW)
For a rotation of 180°
(x, y) ==> (-x, -y)
Change the signs of the x and y coordinates.
ROTATION
Coordinate rules for rotations about the origin (CCW)
For a rotation of 270°
(x, y) ==> (y, -x)
Swap the x and y coordinates and change the sign of the new y coordinate.
Solid of revolution
A three-dimensional figure obtained by rotation a place figure (two-dimensional figure) or curve about a line. Three-dimensional figures can be generated by rotation two-dimensional figures around an imaginary line called a rotation axis.
EX: rotating a two-dimensional triangle about a rotation axis becomes a cone.
EX: rotating a two-dimensional rectangle about a rotation axis becomes a cylinder.
compositions of transformations
When two or more transformations are combined to form a single transformation.
line of symmetry
A figure has a line symmetry if the figure can be mapped onto itself by a *** in a line.
The line of reflection in line symmetry.
