# Practicing Point by Point Transformations

# Practicing Point by Point Transformations

##### Problem 1

1) The figures are congruent. Select **all** the sequences of transformations that would take Figure 1 to Figure 2. Write each corresponding letter in the answer box and separate letters with commas.

a) Translate by directed line segment $AD$. $\quad\quad$ 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 $EF$.

##### Problem 2

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 $CT$.

3) Describe another sequence of transformations that will result in the same image.

##### Problem 3

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

1) Reflect across line segment $AB$.

2) Translate by directed line segment $u$.

##### Problem 4

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

##### Problem 5

6) 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 $C'$.

##### Problem 6

7) 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. Write each corresponding letter in the answer box and separate letters with commas.

a) All sides of the quadrilateral have the same length. $\quad\quad$ 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.

##### Problem 7

8) A quadrilateral has a line of symmetry. Select **all** conclusions that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) All sides of the quadrilateral have the same length. $\quad\quad$ b) All angles of the quadrilateral have the same measure.

c) Two sides of the quadrilateral have the same length. $\quad\quad$d) Two angles of the quadrilateral have the same measure.

e) No sides of the quadrilateral have the same length. $\quad\quad$ f) No angles of the quadrilateral have the same measure.

##### Problem 8

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

##### Problem 9

10) Which statement is true about a translation?