# 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.

Translate by directed line segment \(AD\).

Rotate 180 degrees around point \(E\).

Translate by directed line segment \(AE\) and reflect across \(AC\).

Translate by directed line segment \(CE\) and rotate 90 degrees counterclockwise around point \(E\).

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

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

### Solution

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### Problem 2

- Draw the image of figure \(ACTS\) after a clockwise rotation around point \(T\) using angle \(CTS\) and then a translation by directed line segment \(CT\).
- 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.

- Reflect across line segment \(AB\).
- 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

### 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

### 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.

All sides of the quadrilateral have the same length.

All angles of the quadrilateral have the same measure.

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

### Solution

### Problem 7

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

All sides of the quadrilateral have the same length.

All angles of the quadrilateral have the same measure.

Two sides of the quadrilateral have the same length.

Two angles of the quadrilateral have the same measure.

No sides of the quadrilateral have the same length.

No angles of the quadrilateral have the same measure.

### Solution

### Problem 8

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

### Solution

### Problem 9

Which statement is true about a translation?

A translation rotates a line.

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

A translation takes a line to a perpendicular line.

A translation dilates a line.