rotational symmetry students will be able to identify rotational symmetry. students will be able to...

Rotational Symmetry

•Students will be able to identify rotational symmetry.

•Students will be able to predict the results of a rotation and graph

rotations on a coordinate plane.

•Recall that a circle is composed of 360o.

•When rotating a figure, it is being rotated in a circle; therefore, the angle of rotation will be a factor of 360o.

•360/72 = 5.

•So this figure can be rotated 5 times and still be identical to the original figure before being turned back to its original position.

Vocabulary

• A figure has rotational symmetry if it can be rotated a certain number of degrees about its center and still look like the original.

• The angle of rotation is the degree measure that the figure is rotated.

Explore Rotational Symmetry

1) Turn the square clockwise until it matches the original, ignoring the letters.

2) Continue turning the square, noting the angles at which it matches the original, until the vertices are back to their original position.

Analyze the Results1) How many times did the figure

match itself?

2) Describe the relationship between the number of times the figure matched itself and the angle of rotation.

3) Predict the results of a 90 degree turn of the figure.

Four

The number of times the figure matched itself, 4, and the angle of rotation, 90o, have a product of 360o.

The resulting figure is congruent to the original figure.

Explore Rotational Symmetry

1) Suppose I place a pin on the red dot. Then I turn the figure 90 degrees and trace that figure.

2) Next I turn the figure clockwise another quarter turn to 180 degrees and trace the figure again.

3) Finally I repeat another clockwise quarter turn to 270 degrees and trace.

Analyze the Results

1) Did the figure match itself at any rotation?

2) Does the figure have rotational symmetry?

3) Compare and contrast the figure using line symmetry and rotational symmetry. Does the figure have either?

No

No

The figure has line symmetry in that a line can be drawn so one side mirrors the other. The figure does not have rotational symmetry in that it cannot be turned to match itself except a 360o

turn.

Example of Rotational Symmetry

Which Objects Have Rotational Symmetry?

1) 2)

3) 4)

5) 6)

Practice and Apply: Rally Coach

(One sheet of paper, take turns solving and coaching. Textbook page 564 #8-10.)

Rotations Around a Point

Rotations

• The rotation of a figure is based on a circle, so it can be anywhere from 0 degrees to 360 degrees.

• A rotation can be a clockwise or counter clockwise turn.

• Unless otherwise indicated, the rotation is abut the origin.

Reminder

Clockwise Counterclockwise

Rotate a Figure Clockwise

Rotations Trick!

http://www.youtube.com/watch?v=PWXSNkuvGdk

Rotations Trick!

Rules for rotating when starting with any point (x,y).

DilationsStudents will be able to graph

dilations on a coordinate plane.

Vocabulary

• Dilation- product of enlarging or reducing a figure creating a new image• Center- a fixed point used for measurement when altering the size of a figure

Drawing a dilation by scale factor

1) The center point always remains the same.2) Measure the length of each side to the

center point3) Multiply the scale factor by the length to find

the new length.4) Draw the new point such that the distance is

equal to the length found in step 3.5) Repeat for all points. 6) Connect new points.

Example: Draw the dilation centered at A with scale factor 2

1. A’ = A2. AB = 1cm AD = 2cm AC = 5.7cm3. A’B’ = 1X2 = 2cm A’D’= 2X2 = 4cm A’C’ = 5.7X2 =

11.31cm4. New Points5. Draw Lines

B’

C’

D’

A’

You Try

• Find the new image of the following triangle with a dilation of ½ centered on C.

Dilation centered at (0,0)

• For dilations centered at origin, we don’t need to measure! Just multiply each x and y coordinate by the scale factor to find each new point.

• Ex: Find the new points of a dilation with a scale factor of 1/2.

YOU TRY

Find the new points after a dilation with each of the following scale factors, while centered at the origin.

• Scale factor: 3• Scale factor: 1/3

Find the Scale Factor

1) Choose one point and it’s corresponding image point.

2) Scale factor y coordinate of new point y coordinate of original point

(note: you can use the new x coordinates)

3) Make sure it makes sense! If it is enlarging, then the scale factor should be greater than 1. If it is a reduction, the scale should be less than 1.

Example: Finding the Scale Factor

You Try!