Chapter 7- Transformations Flashcards
A rule that assigns each point of a figure to another point in the plane
Transformation
The result of moving all points of a figure according to a transformation
Image
The original figure that undergoes a transformation
Pure image
A transformation that preserves size and shape
Rigid transformation
Rigid transformations are also called
Isometries
A transformation that does not preserve the original size and shape of the original figure
Nonrigid transformation
An isometry in which each point is slid along a straight path; it is moved by the same translation vector
Translation
A directed line segment from a point to its translated image
Vector
An isometry in which each point is moved by the same angle measure in the same direction along a circular path about a fixed point (known as the ______________ _________)
Rotation
Rotation angle
An isometry in which every point and it’s image are on opposite sides and the same distance from a fixed line (known as the _______ ___ ______________)
Reflection
Line of reflection
The line of reflection is the PERPENDICULAR BISECTOR of every segment joining a point in the original figure with its image
Reflection line conjecture
A figure coincides with itself under a reflection
Reflectional symmetry
A figure coincides with itself under some rotation
Rotational symmetry
Every image is identical to the original figure after a rotation of any multiple of _____
360 degrees
The property that a figure coincides with itself after a rotation of 180 degrees
Point symmetry
A rule that describes how to transform points on a coordinate plane
Either moves something up down right left or reflects
Ordered pair rule
The ordered pair rule (x , y) -> (-x , y) is a reflection across the
Y axis
The ordered pair rule (x , y) -> (x , -y) is a reflection across the
X axis
The ordered pair rule (x , y) -> (-x , -y) is a reflection across the
X and y axes
AND rotation about the origin 180 degrees
The ordered pair rule (x , y) -> (y , x) is a reflection across the
Y=x
The single transformation that gives the same image as a transformation applied to a figure followed by a second transformation applied to the image of the first
Composition
A composition of two reflections across two parallel lines is equivalent to a single translation. In addition, the distance from any point to its second image under the two reflection is twice the distance between the parallel lines
Reflections across parallel lines conjecture
A composition of two reflections across a pair of intersecting lines is equivalent to a single rotation. The angle of rotation is twice the acute angle between the pair of intersection reflection lines
Reflections across intersecting lines conjecture
When you combine a translation with a reflection
Continues to be a rigid transformation
Glide reflections
