How do we graph rotation

Aim: How do we graph rotation?

Rotation

1. An angle of a rotation
2. Direction is counterclock wise or clockwise
3. center of rotation

90 degrees
(A,B) ---> (-B,A)

180 degrees
(A,B)---->(-A,-B)

270 degrees
(A,B)------>(B,-A)

Rotated 180 degrees

Rotated 270 degrees

How do we use the other definitions of transformations

Aim: How do we use the other definitions of transformations ?

Definitions

Glide Reflection: the combination of a reflection in a line and translation along that line.

Orientation:  An arrangement of points relative to one another, after a transformations has occurred.

Isometry: is the transformation of the plane that preserves length.

Invariant: A figure or property that remains unchanged under a transformation of the plane is referred to as ivanant. No variations have occurred.

How to identify composition of transformations

Aim: How do we identify compositions of transformations?

Composition of Transformation
-When 2 or more transformations are combined to from a new translation, in the result is called the Composition of Translation.

Example:

In this image you can see that the traingle was moved from its orignal spot to being reflected off the Y-axis first and then from there is reflected off the X-axis.

You could do any type of combination with these Translations

-Reflection

-Dilation

-Translation

-Rotation

How Do we Graph Dilations?

Aim: How do we Graph Dilations?

A Dilation is a type of transformation that casuse an image to stretch or shrink. It could decrease in size or increase.

•  The scale Factor is the ratio in which the image stretch or shrinks.
• If the factor is greater than 1, then the image will get bigger than the original image.
• If the factor is greater than 0 but less than 1 the image will shrink form the original.
• Multiply the dimensions of the priginal by the scale factors to get the new dimensions of the dilated image.

 Example:
A(-2,-2) --> A'(-4,-4)
B(-1,2) --> B'(-2,4)
C(2,1) --> C' (4,2)
D2

In this figure, it was dilated by 2 from its original image and each point is multiplied by 2.

Some times the image will shrink and this is when the image is dilated by a ratio like

ex: D(1/3) the points will be change from its original to something smaller.

Now try it out:



What are the coordinates of the image of point B under a dilation with center at the origin of scale factor 1/3?

Choose one:
(-1,-3)
(-1,-1)
(-9,-3)
(-9,-9)

How do we identify Transformations?

Aim: How do we identify Transformations?

Transformations are when you move a geometric figure.

There are 4 transformations
-Rotations
-Dilations
-Reflexions
-Translations

-A Translation is when every point is moved the same distance and same direction.
Example: From each point of the triangle move Five units to the right and 3 units down.


-A Dilation is the enlargement or reduction in the size and image.
Example:


-An Rotation is when a figure is turned around a single point.
Example: Move each point 90 degrees Counterclockwise.

- A Reflection is when a figure can be flipped over a line of symmetry.
Example:

Question:

	This graph illustrates a reflection over the x-axis. True False
	Explanation If you folded the graph along the x-axis, the figures would coincide.