Geometry SOL G.3 Transformations Study Guide
Name __________________________________________________ Date_____________Block______
Transformations and Symmetry Review and Study Guide

Things to Know (use your notes, homework, checkpoints, as well as flashcards at
quizlet.com (http://quizlet.com/4695362/geometry-chapter-9-transformations-andsymmetry-flash-cards/). The NY Regents Prep website
(http://www.regentsprep.org/regents/math/geometry/math-GEOMETRY.htm#m5) is
also an EXCELLENT resource.
o Transformations:

translation: moves every point of a figure the same distance in the same
direction; "slide"; pre-image and image are congruent (isometry)


Vectors may be used to describe translations
reflection: creates a mirror image over a line of reflection; "flip"; pre-image and
image are congruent (isometry)

Point reflections are the same as 180 rotations

rotation: turns a figure about a fixed point called the center of rotation; "turn";
pre-image and image are congruent (isometry)

dilation: reduces or enlarges a figure to a similar figure; pre-image and image are
SIMILAR, not congruent
o Transformation Rules (YOU WILL NEED TO KNOW THESE!):

Translations (horizontal a, vertical b): (x, y) → (x + a, y + b) (or vector <a, b>)

Line Reflections:

over x-axis: (x, y) → (x, - y)

over y-axis: (x, y) → (- x, y)

over y  x :

over y   x : (x, y) → (-y, - x)
(x, y) → ( y, x)

Point Reflections: (x, y) → (-x, - y)

Rotations (positive rotations are counterclockwise):


90 : (x, y) → (-y, x)

180 : (x, y) → (-x, - y)

270 (same as - 90 ): (x, y) → (y, - x)
Dilations: for scale factor k, (x, y) → (kx, k y)
Geometry SOL G.3 Transformations Study Guide
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o Symmetry:

line symmetry: occurs when a figure can be mapped onto itself by a reflection over a
line of symmetry; think of folding the paper over this line and getting a match; there
can be no, one, or more than one line of symmetry

rotational symmetry: there is a center point around which the object is turned
(rotated) a certain number of degrees and the object looks the same

point symmetry: same as rotational symmetry with degree of rotation 180o; figure
looks the same upside down.
DO NOT LIMIT YOUR STUDYING ONLY TO PROBLEMS IN THIS STUDY GUIDE!
Example problems:
1) Triangle A’B’C’ is the image of ABC after a translation. Write a rule for the translation. Write
the rule in mapping form, (x, y) → (x +a, x + b), and vector component form, <a, b>.
a)
b)
2) The vertices of ABC are A(-3, 1), B(2, 4), and C(3, 0). Translate ABC using the given vector.
Graph ABC and its image. Label points. Find vertices of transformed image.
a) <2, -3>
b) <-1, -4>
Geometry SOL G.3 Transformations Study Guide
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3) Reflect the polygon over the given line. Label points. Find vertices of transformed image.
a) y-axis
b) x  1
c) y  x
4) Rotate the figures the given number of degrees about the origin. Label all points. Find vertices
of transformed image.
a) 270
b) 180
5) Which statement describes the image:
a) Reflection in line y  1
b) Reflection in line y  x
c) Rotation of 90 about origin
d) Rotation of 180 about origin
e) Translation right 3 units, down 3 units
c) 90
Geometry SOL G.3 Transformations Study Guide
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6) How many lines of symmetry do the figures have? Draw any you find on the figure and write the
number.
a)
b)
c)
d)
e)
7) For each figure in the previous question, specify whether the figure has rotational symmetry. If
so, describe the degrees of rotation. Does the figure have point symmetery? If there is rotational
symmetry, what is the order of the rotation?
8) The vertices of quadrilateral ABCD are A(-3, 0), B(0, 6),
C(3, 6), and D(3, 3). Find the vertices of A’B’C’D’ after a
1
dilation with scale factor . Graph the pre-image and the
3
image, labeling all points. Find vertices of transformed
image.
9) When printed, which of the digits 0 1 2 3 4 5 6 7 8 9 show line symmetry? Which show point
symmetry?
10) Using block printing, name the uppercase letters of the alphabet that show
a) vertical line symmetry
b) horizontal line symmetry
c) point symmetry
Geometry SOL G.3 Transformations Study Guide
Study Guide Answers
1) a) (x + 4, y – 2); <4, -2>
b) (x – 3, y - 1); <-3,-1>
2)
3)
4)
a) A'(-1, 2), B'(-5, 4),
C'(-4, 1)
a) A'(-1, -2), B'(4, 1),
C'(5, -3)
b) A'(3, 2), B'(0, 3),
C'(-3, 2), D(1, -1)
b) A'(-4, -3), B'(1, 0),
C'(2, -4)
b) A'(3, -3), B'(-1, -2),
C'(-1, 1), D'(5, 0)
c) A'(-2, 1), B'(-2, 4),
C'(2, 5), D'(3, 1),
E'(1, -1)
c) A'(2, -1), B'(1, 1),
C'(-2, 1), D'(-2, -2),
E'(-1, -3)
5) d
a) A'(1, 2), B'(2, -4),
C'(0, -1)
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6)
a) 1
b) 1
d) 4
e) 1
c) 8
7) a) no; no b) no; no c) yes (45o, 90o, 135o, 180o, 225o, 270o, 315o); yes; order 8 d) yes (90o, 180o,
270o); yes; order 4 e) no; no
Geometry SOL G.3 Transformations Study Guide
8)
Vertices: A’(-1, 0), B’(0, 2),
C’(1, 2), D’(1, 1)
10)
vertical line symmetry:
AHIMOTUVWXY
horizontal line symmetry:
BCDEHIKOX
point symmetry:
HINOSXZ
9) Line: 0, 3, 8 Point: 0 and 8 (1, too,
depending on how you write it)
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