Big Ideas Math Geometry Chapter 4.1 - 4.3

Vector

a quantity that has both magnitude and direction

Initial Point

the starting point of a vector

Horizontal Component

the horizontal change from the initial point to the terminal point of a vector

Vertical Component

the vertical change from the initial point to the terminal point of a vector

Terminal Point

the ending point of a vector

Component Form

Combines the horizontal and vertical components of a vector in the form of

Transformation

A function that moves or changes a figure in some way to produce a new figure called an image

Image of a Transformation

The new figure after a transformation occurs

Preimage of a Transformation

The original figure prior to a transformation

Translation

A transformation where every point in the pre-image moves the same distance and direction

Similar Figures

if and only if there is a similarity transformation that maps one of the figures onto the other.

Rigid Motion

A transformation that preserves a shapes lengths and angle measures

Postulate 4.1: Translation Postulate

A translation is a rigid motion.

Theorem 4.1: Composition Theorem

The composition of two (or more) rigid motions is a rigid motion.

Composition of Transformations

two or more transformations are combined to form a single transformation

Reflection

A transformation that uses a line like a mirror to reflect a figure.

Line of Reflection

A line that a figure is flipped across to create a mirror image of the original figure

Postulate 4.2: Reflection Postulate

A reflection is a rigid motion.

Glide Reflection

a transformation involving a translation followed by a reflection

Line Symmetry

When a figure can be mapped onto itself by a reflection in a line

Line of Symmetry

a line that divides a figure into two halves that are mirror images of each other

Rotation

A transformation in which a figure is turned about a fixed point

Center of Rotation

A fixed point around which shapes move in a circular motion to a new position.

Angle of Rotation

angle formed by rays drawn from the center of rotation to a point and its image

Postulate 4.3: Rotation Postulate

A rotation is a rigid motion.

Rotational Symmetry

When a figure can be mapped onto itself by a rotation of 180 degrees or less

Center of Symmetry

the center of rotation in a figure that has rotational symmetry

Coordinate Rules for Rotations about the Origin

When a point (a,b) is rotated counterclockwise about the origin, then the following are true:

- Rotation of 90 degrees; (a, b) -> (-b, a)

- Rotation of 180 degrees; (a, b) -> (-a, -b)

- Rotation of 270 degrees; (a, b) -> (b, -a)