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Rigid Transformations: Rotations

Today you will learn more about reflections and learn about two new types of transformations: rotations.

1.33 – TWO REFLECTIONS WITH NONPARALLEL LINES

After the previous lesson, your teammate asks, “What if the lines of reflection are not parallel? Is the result still a translation?” Find ∆EFG and lines v and w below.

a. First visualize the result when ∆EFG is reflected over v to form and then is reflected over w to form

Do you think it will be

another translation?

b. Draw the resulting reflections below. Is the final image a translation of the original triangle? If not, describe the result.

turned image a translation of the original triangle? If not, describe the result.

c image a translation of the original triangle? If not, describe the result.. Using tracing paper, trace the original triangle and rotate it around point P. Verify it lands on

Turns a shape about a point image a translation of the original triangle? If not, describe the result.

Geogebra Rotations image a translation of the original triangle? If not, describe the result.

1.35 – ROTATIONS ON A GRID image a translation of the original triangle? If not, describe the result.

Consider what you know about rotation, a motion that turns a shape about a point. Does it make any difference if a rotation is clockwise ( ) versus counterclockwise ( )? If so, when does it matter? Are there any circumstances when it does not matter? And are there any situations when the rotated image lies exactly on the

original shape?

Investigate these questions as you rotate the shapes below about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

- about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.180° doesn’t matter if you go clockwise or counterclockwise

- 90° counterclockwise is the same as 270 clockwise

- 360° rotates all the way around and matches the original shape

1.35 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.– ROTATIONS ON A GRID

Rotate the triangle by the given degree about the origin.

(5,5) about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

(5,2)

(2,2)

(5,5) about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

(5,2)

(2,2)

(5,5) about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

(5,2)

(2,2)

1.36 – about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above. DEGREE OF ROTATION

State if the rotation about the origin is 90°, 180°, or 270° counter-clockwise.

1.37 – MATCHING SIDES about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

Find the value of each variable in the rotation.

4

x =

z =

3

y =

z + 2

y =

3 + 2

y = 5

4 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.s = 24

s = 6

r =

2s – 3

r =

2(6) – 3

r = 12 – 3

r = 9

1.38 – ROTATION SYMMETRY about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

a. Examine the shape at right. Can this shape be rotated so that its image has the same position and orientation as the original shape? Trace this shape on tracing paper and test your conclusion. If it is possible, where is the point of rotation? How many degrees does it take to match up?

center

120°, 270°, 360°

b. Jessica claims that she can rotate about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.all shapes in such a way that they will not change. How does she do it?

She rotates it a full circle of 360°

c. Since about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.all shapes can be rotated in a full circle without change, that is not a very special quality. However, the shape in part (a) above was special because it could be rotated less than a full circle and still remain unchanged. A shape with this quality is said to have rotation symmetry. But what shapes have rotation symmetry? Examine the shapes below and identify those that have rotation symmetry.

120 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.°,

60°,

180°,

no

240°,

300°,

360°

180 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.°,

360°

no

no about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

120°,

240°,

360°

90 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.°,

180°,

no

270°,

360°

infinite about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

180°,

360°

no about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

no

no about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

no

180 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.°,

360°

72°,

144°,

216°,

288°,

360°

End of Chapter 1 about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

- Group test on Monday
- Individual test on Tuesday

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