Bellringer Work on the Warm Up Sheet NEED: Graphing Sheet Protractor.

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Presentation transcript:

Bellringer Work on the Warm Up Sheet NEED: Graphing Sheet Protractor

Rigid Motions Translations Reflections Rotations Quiz Friday

Reflections Let’s finish out notes on Reflections!

Now try:

Finding the line of reflection Who thinks they can draw it??? A B A’ C C’ B’

To find the line of reflection, find the midpoint of each connecting line. Then connect these midpoints. You can always use the midpoint formula to find the midpoints (like in p. 847 Example A), but a lot of times you will be able to find the midpoint by counting squares.

Let’s move onto our last rigid motion!

Objectives: Draw rotations on a coordinate plane Find the angle of rotation

Rotations Video (2 min) https://www.youtube.com/watch?v=1sxmI4Y1K3s

Rotation Transformation around a point, called the center of rotation.

Rotations Every point and its image are the same distance from the center of rotation.

Rotations All angles with the vertex as the center of rotation formed by a point and its image have the same measure. This angle measure is the angle of rotation

A useful strategy to help you rotate… Physically turn the paper so that you can see where the shape should end up.

NOTE: ROTATIONS ARE ALWAYS COUNTERCLOCKWISE AND AROUND THE ORIGIN UNLESS SPECIFIED OTHERWISE!

Challenge: ROTATE the shape 90o clockwise around the origin. Coordinates: A (-5, 4) B (-5, 1) C (-4, 1) A B C

Challenge: ROTATE the shape 90o clockwise around the origin. Coordinates: A (-5, 4) B (-5, 1) C (-4, 1) B’ A’ A C’ B C

Rotation Activity Perform the three rotations on the figure. After you perform the rotations, try to come up with a rule that represents the rotation!

JAN 24 STOPPED HERE!

Bellringer Work on your warmup sheet!

Rotation Activity Perform the three rotations on the figure. After you perform the rotations, try to come up with a rule that represents the rotation!

Discussion What rule did you come up with for 90° rotation counterclockwise 180° rotation 90° rotation clockwise 360° rotation

Rotation around the origin 90° rotation counterclockwise (x, y)(-y, x) 180° rotation (x, y) (-x, -y) 90° rotation clockwise (x, y)(y, -x) 360° rotation (x, y) (x, y)

These rules only apply to rotation AROUND THE ORIGIN!!

Rotation about origin What is another way to describe a 90° counterclockwise rotation? 90° clockwise rotation? Why do 180° and 360° rotations have no direction?

Draw trapezoid ABCD. Then rotate it 90o counterclockwise. Coordinates: A (1, 6) B (5, 6) C (3, 4) D (1, 4) A B C D A’ D’ C’ B’

Rotate trapezoid ABCD 180o. Coordinates: A (1, 6) B (5, 6) C (3, 4) D (1, 4) A B C D A’ D’ C’ B’

Draw triangle ABC and rotate it 270o. Coordinates: A (2, 7) B (6, 6) C (6, 3) A B C A’ C’ B’

Finding the angle of rotation Estimate: by what angle do you think these shapes are rotated? 80o

Finding the angle of rotation Estimate: By what angle do you think these shapes are rotated? 135o

Review Quiz will cover rotations, reflections, and translations Work on Review Sheet Study with review sheet and homework from this past week.

p. 862, 7 & 8

Measuring it EXACTLY… Read p.862 Example “A” and then try Example “B”.

Homework p.865 (5-8)