Geometry Name: Transformations Test Review Packet

Geometry Unit 3 ? Transformations Test Review Packet

Name: __________________________________

The Unit Test on Transformations contains the following topics:

Isometries

Translations Using Mapping Notation Using Vector Notation Naming Vectors, Component Form, Length of a Vector: 2 + 2

Reflections Over x-axis Over y-axis Over y = x Over y = -x Over vertical lines (x = ____) Over horizontal lines (y = ____)

Rotations 90?, 180?, 270? about origin on coordinate plane Construct rotations using a ruler and protractor

Composition of Transformations on the coordinate plane (does order matter?)

Symmetry

Line Symmetry ? a figure has line symmetry if the figure can be mapped onto itself by a reflection over a line drawn through the figure.

Rotational Symmetry ? a figure has rotational symmetry if the figure can be mapped onto itself by a rotation of 180? or less about the center of the figure.

?

Determining rotational symmetry: # (and all multiples up to 180?)

Dilation ? a similarity transformation in which a figure is enlarged using a scale factor greater than one or reduced using a scale factor between zero and one.

Graph a figure and its dilation on the coordinate plane

Construct the dilation of a figure using a ruler

1. Use the translation (x, y) (x + 2, y ? 5): a. What is the image of D (4, 7)?

b. What is the pre-image of M' (-5, 3)?

2. The vertices of MNO are M (-2, 4), N (-1, 1), and O (3, 3). Graph MNO and its image using prime notation after the translation (x, y) (x + 4, y ? 2):

M': ________

N': ________

O': ________

3. R'S'T' is the image of RST after a translation. Write a rule for the translation in mapping notation and in vector notation.

R

R'

S

S' T

T'

Mapping Notation: Vector Notation:

4. Name the vector, write its component form, and find its length:

a. E

b. T

M

V

5. Write the component form of the vector that describes the translation from S (-3, 2) to S' (9, -7).

6. The vertices of ABC are A (0, 4), B (2, 1) and C (4, 3). Graph and label the coordinates of A'B'C' after each transformation.

a. Translate ABC using the vector -3, 1.

b. Reflect ABC over the x-axis.

c. Reflect ABC over the line y = - x.

d. Reflect ABC over the line y = -1.

7. The vertices of ABC are A (-3, 1), B (1, 1) and C (1, -2). Reflect ABC over the line x = 2. Then reflect A'B'C' over the line y = -3. Graph ABC, A'B'C', and A"B"C". State the coordinates of A"B"C".

A":________

B":________

C":________

8. The coordinates of ABC are A (0, 4), B (3, 6), and C (5, 2). Graph ABC. Rotate ABC 90?, 180?, and 270? counterclockwise about the origin. Record the coordinates after each rotation.

After a 90? Rotation: A' ________ B' _______ C' ________

After a 180? Rotation: A' ________ B' _______ C' ________

After a 270? Rotation: A' ________ B' _______ C' ________

9. List the image of each of the following points after the specified composition of transformations:

a. If point A (-2, 5) is reflected in the y-axis, and then point A' is reflected in the x-axis, the coordinates of point A'' are _________.

b. If point B (-4, -2) is reflected over the line y =- x, and then point B' is rotated 90? counterclockwise about the origin, the coordinates of B'' are _________.

c.

If point C (6, -3) is reflected over the line y = x, and then point C' is rotated 270? counterclockwise

about the origin, the coordinates of C'' are _________.

d. If point D (-2, 10) is rotated 180? about the origin, and then point D' is reflected over the line y=-5, then the coordinates of D'' are ________.

e. If point E (0, 2) is reflected over the x-axis, and then point E' is translated using the vector 1, -2, then the coordinates of E'' are _________.

10. Point P (-6, 2) is transformed to point P' (2, 6). What is the transformation that maps P into P'? Explain.

11. Use a ruler and protractor to rotate RST 140? counterclockwise about point P.

12. The vertices of ABC are A (2, 4), B (7, 6) and C (5, 2). Graph the image of ABC after a composition of the transformations in the order they are listed.

Transformation:

(x, y)(x + 2, y ? 4)

Rotation:

180? about the origin

13. Describe the composition of transformations from ABC to A"B"C".

a.

b.

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