Pre-AP Geometry Chapter 4 Vocab

vector

a quantity that has both direction and magnitude/size

initial point

starting point

terminal point

ending point

component form

combines the horizontal and vertical components

transformation

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

preimage

original figure

translation

moves every point of a figure the same distance in the same direction

rigid motion/isometry

a transformation that preserves length and angle measure

composition of transformations

when 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

reflection in the x-axis

(a, -b)

reflection in the y-axis

(-a, b)

reflection in the line y = x

(b, a)

reflection in the line y = -x

(-b, -a)

glide reflection

a transformation involving a translation followed by a reflection

when the figure can be mapped onto itself by a reflection in a line

line symmetry

rotation

a transformation in which a figure is turned about a fixed point called the center of rotation

angle of rotation

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

rotation of 90

(a, b) → (-b, a)

rotation of 180

(a, b) → (-a, -b)

rotation of 270

(a, b) → (b, -a)

Rotation Postulate

a rotation is a rigid motion

when the figure can be mapped onto itself by a rotation of 180 or less about the center of the figure

rotational symmetry

congruent figures

figures that have the same size and shape

congruence transformation

another name for rigid motion/combination of rigid motions because the preimage and image are congruent

reflections in a parallel line theorem

If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is the same as a translation

reflections in intersecting lines theorem

If lines k and m intersect at point P, then a reflection in line k followed by a reflection in line m is the same as a rotation about point P

Translation Postulate

a translation is a rigid motion

Composition Theorem

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

Reflection Postulate

A reflection is a rigid motion

dilation

when a figure is enlarged or reduced

scale factor

ratio of the lengths of the lengths of the corresponding sides of the image and the preimage

enlargement

scale factor k>1

reduction

scale factor 0<k<1

similarity transformation

a dilation or a composition o rigid motions and dilations

similar figures

same shape but not the same size