Lesson 18

Practicing Point by Point Transformations

Problem 1

The figures are congruent. Select all the sequences of transformations that would take Figure 1 to Figure 2.

A:

Translate by directed line segment $$AD$$.

B:

Rotate 180 degrees around point $$E$$.

C:

Translate by directed line segment $$AE$$ and reflect across $$AC$$.

D:

Translate by directed line segment $$CE$$ and rotate 90 degrees counterclockwise around point $$E$$.

E:

Rotate 180 degrees around point $$C$$, translate by directed line segment $$CE$$, and reflect across segment $$EF$$.

F:

Reflect across segment $$AB$$, rotate clockwise by angle $$BFE$$ using center $$F$$, then reflect across segment $$EF$$.

Solution

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Problem 2

1. Draw the image of figure $$ACTS$$ after a clockwise rotation around point $$T$$ using angle $$CTS$$ and then a translation by directed line segment $$CT$$.
2. Describe another sequence of transformations that will result in the same image.

Solution

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Problem 3

Draw the image of triangle $$ABC$$ after this sequence of rigid transformations.

1. Reflect across line segment $$AB$$.
2. Translate by directed line segment $$u$$.

Solution

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Problem 4

Describe a transformation that takes any point $$A$$ to any point $$B$$.

Solution

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(From Unit 1, Lesson 17.)

Problem 5

Triangle $$ABC$$ is congruent to triangle $$A’B’C’$$.  Describe a sequence of rigid motions that takes $$A$$ to $$A’$$, $$B$$ to $$B’$$, and $$C$$ to $$C’$$.

Solution

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(From Unit 1, Lesson 17.)

Problem 6

A quadrilateral has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this.

A:

All sides of the quadrilateral have the same length.

B:

All angles of the quadrilateral have the same measure.

C:

All rotations take one half of the quadrilateral to the other half of the quadrilateral.

Solution

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(From Unit 1, Lesson 16.)

Problem 7

A quadrilateral has a line of symmetry. Select all conclusions that must be true.

A:

All sides of the quadrilateral have the same length.

B:

All angles of the quadrilateral have the same measure.

C:

Two sides of the quadrilateral have the same length.

D:

Two angles of the quadrilateral have the same measure.

E:

No sides of the quadrilateral have the same length.

F:

No angles of the quadrilateral have the same measure.

Solution

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(From Unit 1, Lesson 15.)

Problem 8

Which segment is the image of $$FG$$ when rotated $$90^\circ$$ clockwise around point $$P$$?

Solution

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(From Unit 1, Lesson 14.)

Problem 9

Which statement is true about a translation?

A:

A translation rotates a line.

B:

A translation takes a line to a parallel line or itself.

C:

A translation takes a line to a perpendicular line.

D:

A translation dilates a line.

Solution

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(From Unit 1, Lesson 12.)