Rotations

Last updated over 7 years ago

14 questions

Note 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. 

Rotations

Rotations

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.