GEOMETRY January 30, 2015. SYMMETRY A line of symmetry can be drawn through an object to create two...

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