Vocab Unit 9 - Transformations

Transformation

A change in the orientation or size of a geometric figure

glide reflection

A composition of a translation and reflection in either order

Reduction

A dilation having a scale factor breather than one

point symmetry

A figure has point symmetry if it has rotational symmetry in exactly 180 degrees

Image

A geometric figure after a transformation

Point of dilation

A given point in the dilation of a figure that is collinear with every point on the pre-image and its corresponding point on the image.

composition

A series of transformations applied to a figure in a given sequence

Reflection

A transformation of a geometric figure in which each point on the preimage has a corresponding point on its image that is equidistant from a given line

Dilation

A transformation that changes the size of a figure by applying the same scale factor to all each sides. Each point on the image is collinear with its corresponding point on the pre-image and the point of dilation

Intersecting Line Reflection Theorem

a rotation is the equivalent of a reflection of a figure in each of two intersecting lines in which the angle of rotation is twice the acute angle of intersection between the lines

isometry (rigid transformation)

a transformation that preserves all segment lengths and angle measures in a geometric figure, thus creating congruent figures.

Translation Theorem

a translation is an isometry such that every point on the pre-image is translated the same distance along the same vector.

Parallel Line Reflection Theorem

a translation is the equivalent of a reflection of a figure in each of two parallel lines in which the distance of translation is twice the distance between the parallel lines

Rotation

an isometric transformation that every point on a figures preimage to its image by a rotation of a specified angle about a fixed point.

Translation

an isometric transformation that maps every point on a figure's preimage to its image by a uni-directional or bi-directional linear movement.

angle of rotation

the angle formed by a point on the preimage of a figure with the point of rotation and the corresponding point on the image.

center of rotation

the fixed point about which a rotation is performed

degree of symmetry

the number of times a figure can be mapped onto itself by rotation in 360 degrees

scale factor

The ratio of the distance of a dilated image from the point of dilation to the distance of its pre-image to the point of dilation

enlargement

a dilation with a scale factor greater than 1

rotational symmetry

a figure has rotational symmetry if it can be mapped onto itself more than once in less than 360 degrees

Preimage

a geometric figure before a transformation

Line symmetry

a geometric figure has line symmetry if each point on the figure has a corresponding point, also on the figure that is equidistant from a line drawn through the figure.

line of reflection

a line in which a geometric figure is reflected.

Reflection Theorem

a reflection is an isometry such that every point on the pre-image is reflected perpendicular to and equidistant from the line of reflection.

Rotation Theorem

a rotation is an isometry such that every point on the pre-image is rotated using the same angle of rotation about the center of rotation, and is equidistant from the center of rotation as are the corresponding image points.