GEOMETRYJanuary 30, 2015

SYMMETRY

•A line of symmetry can be drawn through an object to create two

congruent halves that are mirror images of each other.

•Not all objects have a line of symmetry•Objects can have more than one line of

symmetry

SYMMETRY

Examples of objects with symmetry:

5 lines 4 lines 1 line

DILATIONS

A dilation is a shrink or stretch of an object. Doing this does NOT create an isometry but instead creates a similar

shape to the original

DILATIONS• For coordinate dilations we multiply the vertices by a scalar

•A dilation is a stretch when the dilation factor is greater than 1•A dilation is a shrink when the dilation factor is less than 1

DILATIONS WITH MATRICES•We apply dilations with matrices by using a scalar multiplication:•Example:

with a dilation of factor 4

EXAMPLE 1 with a dilation by factor .

HOMEWORK

Assignment 7-5

COMPOSITION OF TRANSFORMATIONS

• A composition of transformations is applying more than one transformation in the order that they are listed.• Does the order really matter?• Yes• Here is an example:• Take the following points and • Apply the following two transformations a reflection over

the and a translation

COMPOSITIONS OF TRANSFORMATIONS

First lets try it by doing the reflection THEN the translation

• reflect over to

• Then translate to

Now lets try it by doing the translation first THEN doing the reflection

• translated to

• Then reflect over the to

• As you can see the two do NOT result in the same values which indicate that the order does matter.

HOMEWORK

Assignment 7-6