3.
1.
Match the correct definition to the term that corresponds:
1. All sides and angle are congruent a. Rotation 180
2. Flip the coordinates b. Reflection over y = x
3. Negate both the x and y values c. Rotation
4. Flip the coordinates and negate the y-value d. Reduction
5. Two reflections over intersecting lines create a… e. Similar
6. The process of performing more than one f. Rotation 90 Counter transformation on a single pre-image
g. Composition
7. Shapes with the same shape but different sizes…
h. Rotation 90 Clockwise
8. Two reflections over parallel lines create a…
i. Regular
9. Flip the coordinates and negate the x-value
j. Translation
10. Multiplying by a scale factor < 1
Tell whether the transformation appears to be an isometry. Explain.
2.
4.
The dashed-line figure is a translation image of the solid-line figure. Write a rule to describe the translation
5.
Graph the image of each figure under the given translation.
6.
  
3, y

4

7.
  
5, y

1


Each point is reflected across the line indicated. Find the coordinates of each image.
8. A across the x-axis
9. B across the y-axis
10. C across y

1
11. E across y
 
1
12. F across x

Coordinate Geometry Given points M(3, 3), N(5, 2), and O(4, 4), graph

MNO and its reflection image across each line.
13. the y-axis 14. the x-axis
15. x

1 16. y
 
2
Point O is the center of regular hexagon BCDEFG. Find the image of the given point or segment for the given rotation CLOCKWISE.
17.
120
°
rotation of F about O.
18.
180 ° rotation of B about O.
19.
300 ° rotation of BG about O

Use the figure at the right for Exercises 13–15. Point T is the center of the regular decagon. (Go CLOCKWISE)
20.
What is the angle of rotation that maps D to A?
21.
What is the angle of rotation that maps B to H?
22.
Describe a composition of rotations that maps A to E.
23.
A pie is cut into 12 equal slices. What is the angle of rotation about the center that will map a piece of pie to a piece that is two slices away from it?
24.

RST has vertices at R (0, 3), S (4, 0), and T (0, 0). Find the coordinates of the vertices after a 90º clockwise rotation about T.
25.

FGH has vertices F (−1, 2), G (0, 0), and H (3, −1). Find the coordinates of the vertices after a 90 ° counterclockwise rotation about G.
Tell what type(s) of symmetry each figure has. If it has line symmetry, sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation.
26. 27. 28.
Tell whether each three-dimensional object has reflectional symmetry in a plane, rotational
symmetry about a line, or both.
29. a starfish with five legs
30. Which capital letters in the English alphabet have rotational symmetry?
Find the image of each letter for a reflection, first across line ℓ, and then across line m. Is the resulting transformation a translation or a rotation? For a translation, describe the distance and direction. For a rotation, tell the center of rotation and the angle of rotation.
1. 2. ℓ ℓ

Graph

DML and its glide reflection image for the given translation and glide reflection image reflection line.
3. ( x, y ) → ( x + 3, y ); x = 0 4. ( x, y ) → ( x

1, y ); y = 1
5. ( x, y ) → ( x , y + 1); x = 2 6. ( x, y ) → ( x + 3, y + 3); y = x
7.
In which types of isometries are the image and preimage in the same orientation?
8.
A triangle is reflected across line ℓ and then across line m. If this composition of reflections is a translation, what is true about m and ℓ ?
Graph
AB and its image
  after a reflection across ℓ
1
and then across ℓ
2
.
Is the resulting transformation a translation or a rotation? For a translation, describe the direction and distance. For a rotation, tell the center of rotation and the angle of rotation.
13. A (

3, 4), B (

1, 0); 14. A (

5, 2), B (

3, 6); ℓ
1
: x = 1; ℓ
2
: y =

1 ℓ
1
: x =

2; ℓ
2
: x = 3

P → P ′ (2, 3) by a glide reflection for the given translation and reflection line. What are the coordinates of P?
16.
( x, y ) → ( x, y + 2); y = 0 17. ( x, y ) → ( x + 3, y

2); y = x
Graph ∆ABC and its glide reflection image for the given translation and reflection line.
4. (x, y)  (x

2, y); y = 0
To start, translate the vertices of ∆ABC to:
Then, reflect ∆A’B’C’ across .
5. (x, y)

(x, y

3); x = 0 6. (x, y)

(x + 1, y

1); y =

1
11. Graph a Glide reflection with translation
( , ) ( x 4, ) and reflection across the line
y =  2
Coordinates of M”N”P”:
M” = _________ N” = ___________ P” = __________
12.Graph pentagon ABCDE and its image
A′B′C′D′E′ for a dilation with center (0, 0) and a scale factor of 2. The vertices of ABCDE are:
A(0, 3), B(3, 3), C(3, 0), D(0,  2), E(  1, 0).
A’ = ______ B’ = ________ C’ = ________
D’ = ______ E’ = ________