Lesson 18

Practicing Point by Point Transformations

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Problem 1

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

Two figures on a grid.
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.
A figure formed by 3 line segments, looks like the letter U. 4 points on the endpoints of the segments. Starting at the top left, A. Moving downard, C. Moving to the right, T. Moving upward, S.

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 \(u\).
Triangle A B C.

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 \(C’\).

Congruent triangles A B C and A prime B prime C prime.

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 \(P\)?

Segments on a grid.

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.)