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Geometry – Chapter 4 Test Review
Standards/Goals:
 E.1.a.: I can determine points or lines of symmetry and apply the properties of symmetry to figures.
 G.CO.4./ E.1.e.: I can identify and draw images of transformations and use their properties to solve
problems.
 G.CO.5.: I can draw a transformed figure and describe the sequence of transformations that were used
to carry the given figure onto the other.
 G.CO.2./ G.1.e.: I can determine the effect of reflections, rotations, translations, and dilations and their
compositions on the coordinate plane.
 G.CO.3.: I can describe the rotations and/or reflections of various polygons that carry it onto itself.
 G.CO.7.: I can understand the definition of congruence and how it relates to a transformation that is a
‘rigid motion’.
 G.SRT.1a: I can understand the idea of a dilation in the context of transformations.
o I can identify the scale factor from a dilation.
o I can understand the image, pre-image, scale factor, center, and similar figures as how they
relate to transformations.
 G.SRT.1b: I can explain how a scale factor shows how much larger or smaller a figure becomes after a
dilation.
IMPORTANT VOCABULARY
Transformation
Rigid Motion/
Isometry
Pre-Image
Image
Translation
Reflection
Line of
Reflection
Rotation
Clockwise/
Counterclockwise
Ratio
Protractor
Dilation
Line of symmetry
Scale
Factor
Rotational
symmetry
Reduction
Symmetry
Magnitude of
symmetry
Point symmetry
Plane
symmetry
Axis symmetry
Similar
figures
line
(reflectional)
symmetry
Quadratics
Parabola
Standard
form of
an
quadratic
equation
Vertex
Vertex form of of
an quadratic
equation
Axis of
symmetry
Maximum/Minimum
Values
Parent
function
Equidistant
Enlargement
#1. Given A(2, -6), under which reflection is
a. A’(2, 6)?
b. A’(-2, -6)?
#2. How many lines of symmetry does an equilateral triangle have? A regular pentagon?
#3. What type of dilation occurs with a scale factor of
5
a. 2?
b.
2
?
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Order of
symmetry
2
#4. Multiple Choice: Which type of transformation moves all points the same distance in the same
direction?
a. Rotation
b. Translation
c. Reflection
d. Dilation
#5. Mary’s old television had 82 pixels across the screen. Her new television has 205 pixels. Find the
scale factor by which she increased her screen size.
#6. A point Y with coordinates (-8, 6) is rotated about the origin. What would the resulting coordinates
be for the following rotations?
a. 90°
b. 180°
c. 270°
d. 360°
#7. Find the magnitude of the rotational symmetry in a regular octagon?
#8. Find the coordinates of K’ with K(-5, 7) for a dilation centered at the origin with a scale factor of
a. 3
b. ½
#9. Of the transformations we have learned, which one turns every point of the pre image through a
specified angle and direction about a fixed point?
#10. What is the image of A(-6, 9) under the following translations?
a. (4, -5)
b. (-10, 1)
c. (-5, -3)
#11. Multiple Choice: Which of the following is true for an isometry?
a. The preimage and image are congruent
b. The preimage is larger than the image
c. The preimage is smaller than the image
d. The preimage is in the same position as the image.
#12. Multiple Choice: An isometry is a transformation of an object in which the original object and its
image are congruent. Which transformation is NOT always an isometry?
a. Dilation
b. Reflection
c. Rotation
d. Translation
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#13. Which of the following letters have point symmetry?
A B C
L M N
W X Y
D
O
Z
E
P
F
Q
G
R
H
S
I
T
J
U
K
V
#14. Multiple Choice: Which letter has rotational symmetry, but NOT reflectional symmetry?
a. A b. C
c. O
d. Z
#15. Which type of symmetry does the following figures have?
a.
#16. Point 0 is the center of regular hexagon ABCDEF
Determine the following:
a. 180° rotation of F about O.
b. 120˚ rotation of F about 0.
c. 240° rotation of B about O
d. 300° rotation of BG about O.
#17. Multiple Choice: Which action represents the reflection of a figure?
a. Slide
b. shift
c. turn
d. flip.
#18. The coordinates of point A are (-3, b). Point B is created by reflecting point A across the x-axis and
then translating the image point 4 units to the right. What are the coordinates of point B?
#19. The coordinates of point B are (a, 5). Point C is created by reflecting point B across the x-axis and
then translating the image point 7 units to the right and then 5 units up. What are the coordinates of
point C?
#20. Suppose you draw a dilation of this arrow with a scale factor of 5. How does the area of the arrow
after the dilation compare to the area of the original area?
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#21. Consider the following quadratic equation to answer the questions.
𝒚 = −𝟑𝒙𝟐 + 𝟏𝟖𝒙 − 𝟕?
a. What is the vertex of the parabola
b. What is the axis of symmetry of the parabola given above?
c. What is the y-intercept?
d. Does the parabola have a minimum or a maximum? Where is the min/max?
#26. Graph each image of the figure using the transformation given.