SAU5 Rigid Motion Vocabulary and Key Concepts

Scale Factor

In two similar geometric figures, the ratio of their corresponding sides is called the scale factor.

Transformations

Is a function, or mapping, that results in a change in the position, shape or size of the figure

Line of Reflection

Is a line that a preimage is reflected across, it is in the center of the preimage and image.

Composition of Transformation

The combination of two or more transformations to form a single transformation

counter clockwise

In the direction opposite to the rotation of the hands of a clock.(positive angle measure)

polygon

A closed plane figure made up of line segments

Point of Rotation

A point around which a figure is rotated either clockwise or counterclockwise.

Point of Symmetry

A point around which the image can rotate upon itself

Enlargement

A scale factor greater than n>1

Reduction

A scale factor greater than zero and less than one. 0<n<1

Rigid Motion

A transformation that preserves distance and angle measure. The distance between any two points of the preimage is the same distance between the corresponding points of the image. The angles of the preimage and the corresponding angles of the image are congruent.

Translation

A transformations of a plane that slides every point of a figure the same distance in the same direction. Described as a direct isometry involving rigid motion of the shape. The image and preimage have the same orientation to the x and y axis, and corresponding parts remain congruent to the preimage.

Reflection

An isometry where the points of the preimage and corresponding points of the image are equidistant from the line of reflection. A transformation that acts like a mirror: It swaps all pairs of points that are on exactly opposite.

Angles of Rotation

Angle of rotation is the number of degrees a figure rotates.

Center of Rotation

Center of rotation. The point that a figure rotates 𝑥° about.

Congruence Transformations

Compositions of rigid motions. Since these transformations take figures to congruent figures.

Angle of Symmetry

For a regular polygon 360/n where n is number of sides

Corresponding Parts

Have a one-to-one relationship with one another. In congruent polygons, the pairs of sides which can be superimposed on one another. In similar polygons, the ratio of the length of a side on the larger polygon to the length of is corresponding side on the smaller polygon

Counter-Clockwise

In the direction opposite to the rotation of the hands of a clock.

Carry onto self

It means the image lines up perfectly with the pre-image.

Line of Symmetry

Lines on which an image can reflect itself

Preserves

Retains the same shape and measure

Glide Reflection

The composition of translations (a glide) and a reflection across a line parallel to the direction of the translation. This transformation is commutative. Translate first then reflect or Reflect first then translate.

Orientation

The direction that image to preimage appears

Orientation

The direction that material appears on a page when printed.

Preimage

The original shape in a transformation.

Congruent Shapes

Two figures are congruent if and only if there is a sequence of one-to-one correspondence that maps one figure onto the other.

Symmetry

When an object is invariant to a transformation. Invariant to remain unchanged when transformations of a certain type are applied to the objects. A figure is symmetric if there is an isometry that maps the figure onto itself. A figure that can be a reflection of itself has a line of symmetry. A figure can have multiple lines of symmetry.

Image

a copy of an object formed by a transformation.

Regular Polygon

a polygon that is both equilateral and equiangular

Vector

a quantity that has both magnitude and direction

Rotational Symmetry

if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same. Regular polygon rule n = 2, 180°.

Reflection Symmetry

if there is at least one line which splits the image in half so that one side is the mirror image of the other

Clockwise

in the same direction as the rotating hands of a clock

clockwise

in the same direction as the rotating hands of a clock (negative angle measure)

Center of Dilation

is a fixed point in the plane about which all points are expanded or contracted.

Mappings

is a function that takes points as an input, and produces a transformed point as the output.

Isometry

is a transformation in which preimage and image are congruent

Reflection over a line

is a transformation in which the distance of each point of the pre-image to the line is congruent to the distance of the corresponding points of the reflected image from the line, the reflected image is on the opposite side of the line.

Dilation

is a transformation that produces an image that is the same shape as the preimage but is either a proportional enlargement or reduction. The proportion is the Scale Factor, k . It stretches (enlarges) or shrinks (reduces). The center of dilation is a fixed point in the plane about which all points are expanded (k>1) or contracted (0<k<1).

Rotation

is an isometric turning of an object around a center (or point) of rotation

point symmetry

the common point of reflection for all points of a figure

mapping notation

transform every item in the domain" (and "domain" means "group of things you're transforming"). So, the "mapping notation" you've mentioned, like (x, y) → (x+1, y+1), is a way we can express any kind of transformation in the geometric plane.

Prime Notation

used to identify image points