Chapter 6: Transformations

Chapter 6: Transformations

Time for review...Get your Notes ready!

Poll

How many of you are prepared for a chapter test on Transformations?

• For sure

• Absolutely!

• Kind Of...?

• Not @ ALL!

Transformations:

• There are four types of transformations, can you name them?

• Each type has its own kind of notation related to the type of movement or adjustment made to a figure, from "pre-image - to image"

Translations

Remember , that moving a figure from its original position is called the "pre-image." Mathematically we can use a 'translation notation' to move a figure : see the examples to the right ...

Reflection ....a.k.a "the opposite of"

• Reflection over the x-axis: (x, y) - (x, -y)

• Reflection over the y - axis: (x, y) - (-x, y)

• Review the diagram to the right.

Rotations...about the origin (0,0)

• 90 degree CW (x, y) --> (y, -x)

• 180 degree (x, y) --> (-x, -y)

• 270 CW OR 90degree CCW (x,y) --> (-y, x)

• Review the diagram to the right.

Dilation ...scale factor = k

• An enlargement: Multiply by a whole number k, as k > 1

• A reduction: multiply by a fraction k, as 0 > k > 1

• (x , y) --> (kx, ky)

• To go from the pre-image to the final image , you multiply by "k" the scale factor.

Multiple Select

The following is a representation of...Triangle ABC to A'B'C'.

• Rotation

• Translation

• Dilation

• Reflection

Multiple Select

Which is a reflection y-axis?

• A

• B

• C

• D

Multiple Select

Rotate P(2, -9) 90° counterclockwise about the origin and identify P'.

• (-9, 2)

• (-2, 9)

• (2, -9)

• (9, 2)

Multiple Select

State the quadrant in which a triangle will lie if it is in the fourth quadrant and is rotated 180° about the origin.

• I

• III

• IV

• II

Multiple Select

A triangle has vertices A(0, 0), B (9, 4), and C(–2, 10). What are the coordinates of the triangle after a dilation with a scale factor of 1/2?

• A'(0, 0), B'(4.5, 2), and C'(–1, 5)

• A'(0, 0), B'(18, 8), and C'(–4, 20)

• A'(0, 0), B'(3, 2), and C'(0, 5)

• A'(0, 0), B'(–4.5, –2), and C'(1, 5).

Multiple Select

Graph with vertices A(1, 2), B(4, 1), C(5, 3). Then graph the image of triangle A'B'C' with a scale factor of 2.

• A

• B

• C

• D

Now that you have completed this brief quiz, give yourself some time and complete this Preview Review Quiz (for credit).

Types of Transformations...

Poll

Now that you have gone through the review, how do you feel about your skills for the up coming chapter 6 test?

• Great!

• Awful?

• Ready.

• Nearly prepared.