Polygons and Transformations

Unit 2

Essential Questions

1.) How can you change a figure’s position without changing its size and shape?

2.) What process is used to perform a reflection across a line?

What are Transformations? (Ch. 9.1)Definition:

The methodical movement of a geometric figure on a plane. The starting figure is called a “pre-image” and the resulting figure is called an “image”.

Characteristics and Tendencies:

• There are 4 types: Translation, Rotation, Reflection, and Dilation.

• Follows the same naming/labeling rules used with ≅ figures

• Translation, Rotation, and Reflection • are called the Rigid• Transformations.

Example:∆ABC → ∆A’B’C’ Non-

Examples: ABCD → A’C’B’D’

Transformations

A Foldable for your Journal

The Top FlapIII

III IV

(+,+)(-,+)

(-,-) (+,-)

X-Axis

Left and Right

- +

Y-Axis

Down and Up

- +

Coordinates(x,y)

Pre-Image → ImageA → A’Original → ResultBefore → After

Problem 3 (pg 547)

T<-2,-5> (∆PQR) Item Being

Affected

Translation

Change of X Value

Change of Y Value

Could Also be represented as:

(x-2, y-5)

Left 2 and Down 5

Inside the top flap

Summarize what is happening to the transformation in your own words!

What are Reflections? (Ch. 9.2)

• A reflection over a line k is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line.

• Remember that a reflection is a flip.

• When reflecting over the x axis, the sign of y changes

• When reflecting over the y axis, the sign of x changes

• The notation for reflections: rk

• The image keeps the same dimensions as the preimage

Lets take a look at an example

1.) Look at this problem and let’s go over it! (remember to put this cutout in your journal, not in your foldable)

Ry-axis( ABC)

Reflection

The line you arereflecting over The item being

affected

X Y New X

New Y

A -3 4 A’ 3 4

B 0 1 B’ 0 1

C 4 2 C’ -4 2

Since we’re reflecting over the y-axis, only the X’s are affected

Now let’s go back to our foldable….On the Inside of the 2nd flap

Summary:

Vertical or Horizontal Axis:

Count from each vertex of the pre-image to the axis of reflection and then count the same value again.

y=x OR y=-x

Switch the x and y values for each vertex in the pre-image.

BOTH versions result in points that are equidistant from the axis of reflection.

F

G

H

F’

H’

G’

On the Front of the Third PageFrom Pg 557 in Textbook

R y-axis (∆FGH)Reflection Figure Effected Axis of Reflection

Reflection (Flip)

F

G

H

F’

H’

G’

R y=-1 (∆FGH)

F

G

HF’

H’

G’

R y=x (∆FGH)(2,2

)

(4,-3)

(-2,-1)

(-1,-2)

(-3,4)

(2,2)

Inside the top flap Summarize in your own words how to reflect an object!

Now Let’s Practice!

On the Back of the Third Page

Summary:

Based on the required rotation to each vertex, determine the resulting Quadrant, switch the x and y values if necessary, and then apply the – and + values as appropriate.

On the Front of the Fourth PageFrom Pg 565 in Textbook

r (90˚, O) (∆FGH)Figure Effected

Rotation Degree of Rotation

Center of Rotation (in

this case it is origin)

Rotation (Flip)

0˚=(x,y)90˚=(y,x)

180˚=(x,y)270˚=(y,x)360˚=(x,y)

Every Quadrant is a total of 90˚

F

J

H

F’

H’

G’

Quadrants

III

III IV

(+,+)

(-,+)

(-,-) (+,-)

Counter – ClockwisePositive Rotation

ClockwiseNegative Rotation

G

J’