Rotations

by David Kwan

| 14 QuestionsNote from the author:

This Formative is by: Brian Gervase

This lesson introduces students to the formal definition of a rotation. Students have an opportunity to play with rotations in a guided fashion using Geogebra applets.

This lesson will introduce us to rotations and the vocabulary we will need to discuss them.

Start by trying out the example below. Be sure to use the angle slider to play and also change the checkbox to see what happens. You will be asked about your observations below.

1

1

What direction does a POSITIVE rotation move? That is, as the rotation angle gets larger, which direction is the object moving?

Clockwise

Counter-clockwise

2

1

What are the 'inputs' needed to perform a rotation? Select all that may apply.

Angle of rotation

Center of rotation

Color of the original object

Number of points on the original object

3

1

ABCD is congruent to A'B'C'D'.

True

False

In the sketch above, check the box labeled "Rotate about O". Now, construct a circle with center O which goes thru point A. Next, construct another circle with center O which goes thru point C.

Use the angle slider to again move the rotated object.

4

1

What other point(s) are on your circles? Why do you think this is true?

5

1

If you were to construct another circle centered at O and goes thru point D, what other point would be on the circle?

A'

B'

C'

D'

6

1

When ABCD is rotated 360 degrees about point O, all four points 'travel' the same distance?

True

False

7

1

When ABCD is rotated 360 degrees about point O, all four points 'travel' the same amount of degrees?

True

False

8

1

Explain why your answers above are different (they should be!). For example, explain why points D and B travel different distances but cover the same number of degrees.

9

1

After rotating the original square by 90 degrees, it is possible to put the new square image back on top of the original using only TRANSLATIONS.

True

False

10

1

Janice claims that to rotate a triangle ABC, she can simply rotate points A, B and C to the proper place and then "connect the points" to create the new triangle image.

True

False

11

1

Ralph has a music record album which is spinning at a rate of 45 revolutions per minute. Near the center he has a point labeled P and near the outer edge of the record he has a point labeled M. He claims both points are moving at the same speed, which is 45 revolutions per minute.

True

False

12

1

Peter disagrees with Ralph. He claims that point M is actually moving faster than point P. After much deliberation, Ralph successfully convinces Peter that "each point is going around the circle in the same amount of time, therefore they are moving at the same speed."

Which best decribes the truth here? Choose all that apply.

M is moving faster than P, when measured in inches/minute

P is moving faster than M, when measured in inches/minute

M and P are moving at the same speed, when measured in inches/minute

M and P are moving at the same speed, when measured in revolutions/minute

13

1

If point P is exactly 1 inch from the center of the spinning record, how fast is point P moving measured in inches per minute. Round to the nearest whole number.

14

1

If point M is exactly 3 inches from the center of the spinning record, how fast is point M moving measured in inches per minute. Round to the nearest whole number.

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