Studied by 16 people
Isometry
A transformation that does not change the shape or size of a figure
Types of Isometries
Reflection, translation, and rotation
Other Names for Isometries
Congruence transformation or rigid motions
Preimage
The original figure
Image
Resulting figure
Reflection
A transformation across a line which is the perpendicular bisector of each segment joining each point and its image
Reflection across the x-axis
A(x,y)→A’(x,-y)
Reflection across the y-axis
A(x,y)→A’(-x,y)
Reflection across the line y=x
A(x,y)→A’(y,x)
Translation
A transformation where all the points of a figure are moved the same direction. The image is congruent to the preimage and when transformed along a vector the image has the same length as the vector and is parallel to the vector.
Translation along a Vector
A(x,y)→A’(x+a,y+b)
Rotation
A transformation that turns a figure around a fixed point.
Center of Rotation
The fixed point around which a rotation is made
Line of Reflection
A straight line across which a reflection is made
Rotation by 90 about the Origin
A(x,y)→A’(-y,x)
Rotation by 180 about the Origin
A(x,y)→A’(-x,-y)
Composition of Transformation
One transformation followed by another
Glide Reflection
The composition of a translation and a reflection across a line parallel to the translation vector
Isometry
A composition of two isometries is a(n) _______.
Translation
The composition of two reflections across two parallel lines is equivalent to a(n) _______.
Rotation
The composition of two reflections across two intersecting lines is equivalent to a(n) __________.
Reflections
Any translation or rotation is equivalent to a composition of two ___________.
Symmetry
A figure has __________ if there is a transformation of the figure such that the image coincides with the preimage
Line Symmetry
A figure has ______ if it can be reflected across a line so that the image coincides with the preimage
Line of Symmetry
Divides the figure into two congruent halves
Rotational Symmetry
A figure has ___________ if it can be rotated about a point by an angle greater than 0 and less than 360 so that the image coincides with the preimage
Plane Symmetry
A three-dimensional figure has ________ if a plane can divide the figure into two congruent reflected halves
