Chapter 8:Transformations

By Yujie Jenny Ma

Lesson 1

Vocabulary:

Transformation – a one-to-one correspondence between two sets of points

Pre-image – the original figure

Image – figure after transformation

Vocabulary cont’d

Center of dilation – the point which is used as a reference point for a dilation

Line of reflection – the mirror; the line over which an image is reflected

Isometry – a transformation that preserves distance and angle measure

Translation – a slide; a transformation where all the points in the image are the same distance from their corresponding points in the pre-image

Reflection – a transformation where all points on the image are the same distance from the line of reflection as their corresponding points in the pre-image

Rotation – a transformation where a figure is shifted by an angle around a specified point

Dilation – a transformation where a figure is increased or decreased in size by a factor (the points of the image are at the distance of their corresponding points, on the pre-image, from the center of dilation multiplied by the factor)

Lesson 2

A reflection through line l of point P creates P’. Line l is then the perpendicular bisector of segment PP’.

Construction 8 – reflecting a point across a line

Defining other transformations through reflections

Translation – the composite of two successive reflections through parallel lines

Rotation – the composite of two successive reflections through intersecting lines› Center of rotation – the point about which a

rotation occurs› Magnitude – the measure of the angle through

which a point of the original figure turns to coincide with its rotation image

Lesson 3

Vocabulary: Congruent – two figures are such if there exists an

isometry such that one figure is the image of the other

Glide Reflection – the composite of a translation and a reflection over a line parallel to the direction of the translation (in a sense, three or some greater odd number of reflections)

Mirror Image – created by an odd number of reflections, two figures are the reverse of one another

Glide Reflection

They’re congruent.

Lesson 4

Vocabulary: Rotation symmetry – a figure possesses this

characteristic, with respect to a point, iff it coincides exactly with its rotation image when rotated less than 360˚ about the specific point (the center of the figure is usually said point)› A figure has point symmetry if it looks exactly the same

turned upside down

n-fold rotation symmetry – a figure has this iff the smallest angle through which it can be turned to look exactly the same is 360˚/n› A figure with point symmetry has 2-fold symmetry

Vocabulary cont’d

Reflection (line) symmetry – a figure has this, with respect to a line, iff it coincides with its reflection image through the line› The line is sometimes called the axis

Translation symmetry – a patter has such iff it coincides with a translation image

Rotation symmetry

Reflection symmetry

Translation symmetry