GEOMETRY MOCK EXAM 1. What term describes a transformation that does
not change a figure's size or shape?
6. A regular polygon with n sides is carried onto
itselfby a positive rotation about its center that
is a multiple of 60°, but less than 360°.
Which could NOT be the value of n?
(A) similarity
•
isometry
(A) 3
.5
(C) collinearity
(B) 4
(D) symmetry
\'2-J
(D) 6
For questions 2-4, use the diagram showing
parallelogram ABeD.
7. In the diagram, gil hand B lies on line g.
IOcm
r__-~A,-_"",
5cm
+-+
2. A reflection across EG carries parallelogram
ABeD onto itself.
A
A'
(A) True
•
False
3. A rotation of 90° about I carries parallelogram
ABeD onto itself.
g
h
(A) True
The figure ABe is reflected across line g, and
its image is reflected across line h. What is the
distance from line g to the final image of point
A?
•
(A) 5 cm
False
4. A rotation of 180° about I carries
parallelogram ABeD onto itself.
• True
(B) False
5. Which of these is equivalent to a translation?
(B) 15 cm
(C) 20 em
•
25 em
8. What is the image of the point (-4, 6) under
the transformation T(x,y) ~(-y,x)?
(A) a reflection across one line
(A) (6,4)
(B) a composition of two reflections across
intersecting lines
_ (-6,-4)
•
a composition of two reflections across
parallel lines
(C) (4,6)
(D) (-4, -6)
9. A figure is rotated about the origin by 180°,
then is translated 4 units right and one unit up.
Which describes the results 0 f the two
\
transformations?
\ .:
For questions 13-16, determine if the described
transformation(s) is/are an isometry.
13. A reflection is an isometry.
I
•
(x,y)~(-x+4, y+l)
• True
(B) False
(B) (x,y)~(-x 4,-y-1)
(C) (x,y) ~ (-y+4, x+ 1)
14. A composition oftwo reflections is an isometry. (D) (x,y)~(-y-4,x+l)
• True
(B) False
10. The point A(4, 3) is rotated -90° about the
origin. In which quadrant is A ?
I
(A) I
15. A dilation is an isometry.
-"
\
(A) True
(B) II
•
1'\'
(C) III
•
IV
11. A figure is reflected across the line y = 2, then
reflected across the line y = 4. Which single
1\(2,'71
transformation results in the same image?
(A) a reflection across the line y
(B) a reflection across the line y
~3
~6
+'
:
'
.
",1
~
:1
l J{
C
False
16. A composition of a rotation and a dilation is an
isometry.
(A) True
•
False
i"
(C) a translation 2 units up
4A •
•
\
a translation 4 units up
(1.T\)
17. In MBC, M is the midpoint of AB and N is the midpoint of AC. For which type of triangle is MN 12. Point A' is the image of point A under a
transformation T. Line f is the perpendicular
bisector of AA' at point M. Which describes
the transformation T?
•
'(
1;
a reflection across f
(B) a 90° rotation about M
(C) a translation by the vector from A to M
(D) a dilation about M with scale factor 2
~ BC ?
2
(A) equilateral only
(B) isosceles only
f)" M/ " ·\~~C
(C) scalene only
•
any triangle
18. After a figure is rotated, p' = P. Which statement(s) could be true? (A) The center of rotation is P.
(B) The angle of rotation is a multiple of
360°.
•
Either A or B or both.
(D) Neither A nor B.
19. Use the diagram.
23. Given point A is located at (1,3). What is the
final image of A after this series of
transformations?
m
(1) Reflect A across the y axis.
(2) Translate the image such that
k
(x,y)----)-(x-4,y+2)·11
J
p,\
(A) (-1,-3)
_.. . --1
(B) (-3, 5)
(C) (-3, -1)
•
A
\
(-',1)T (\i~)
1
I
i
(-5,5)
-
For questions 24-27, use the diagram where B is the
reflection of A across P Q.
Which series ofreflections would result in a
rotation of-44 0 about A?
(A) reflect across k, then reflect across f
•
,*"
reflect across f, then reflect across k
(C) reflect across f. then reflect across m
A
(D) reflect across m, then reflect across t
For questions 20-21, a transformation S is defined
as (x,y)----)-(3x, y-l).
20. The pre-image of A'(3,
6)
under S is A(9,
5).
(A) True
•
False
24. PA
PB
• True
(B) False
.­
25. PQ .1 AB
• True
(B) False
21. S is an isometry.
(A) True
•
False
26. AQ QB
• True
(B) False
22. Which transformation does NOT preserve the
orientation of a figure?
(A) dilation
• reflection
(C) rotation
(D) translation
27. PQ= 1 AB 2
(A) True
•
False
./
B
28. Use the figure.
For questions 29-31, use the diagram where ABCD
-is a quadrilateral with AB II CD and AD II BC.
Y
Diagonals A C and BD intersect at E .
£.
.V
'\" ......
·
....
~
~ y . . . . t..· ....
____-r______-..A
\
•
£.
......
\
•
•
....
'.
rs
....
......... . ...
I· ..
.. ..
x
..
·
.. ·~6 f .. •
C
A transformation T is defined as
(x,y) ~ (x, - y). Which shows the image of
29. figure under T?
f:.CBE~MBE
(A) True
y
(A)
•
30. False
MDE~MBE
(A) True
•
False
31. f:.CDE ~ !::.ABE
• True
(B) False
(B) 32. A figure is transformed in the plane such that
no point maps to itself What type of
transformation must this be?
(A) dilation
(B) reflection
•
(C) rotation
•
x
translation
For questions 33-36, detennine if the mapping is an
isometry.
33.
(x,y) ~(x, y+2)
•
39. A rotation of 90° about P results in pi = P.
•
True
I .,
(B) False
; \"" t1;'­
is an isometry.
True
40. A translation by the vector (-6, 0) results in
(B) False
34.
pI=P.
(x,y) ~ (~x, y)
•
is an isometry.
(A) True
•
False
41. A reflection about the x axis results in pi
True
(B) False
35.
(x,y) ~ (y, x)
•
= P.
•
True
(B) False
is an isometry.
For questions 42-43, use the diagram which shows
MBC has been reflected across an unknown line f.,
True
then reflected across line m to produce M"B"C".
y
(B) False
36.
For questions 39-41, point P is located at (6, 0) and
undergoes a transfonnation.
(x,y) ~ (2x, y)
is an isometry.
(A) True
•
False
For questions 37-38, detennine the truth of the
statements about rotations.
37. Rotations preserve the orientation of a figure.
•
True
(B) False
38. Under a rotation, no point can map to itself
(A) True
•
False
42. The equation of line f. is x
--0.5.
.../
•
True
(B) False
43. If MBC were reflected across line m first,
then reflected across 'line f. to produce
M"B"C', the equation of line f. would be x =
0.5.
•
True
(B) False
For questions 44-46, consider a triangle MBC
that has been transformed through rigid motions
and its image compared to AXYZ . Determine if
the given information is sufficient to draw the
provided conclusion.
Given
LA:;; LX
44.
Conclusion
LB:;; LY
Look at these three figures.
I
LC:;; LZ
(A) True
•
II
False
Given
LA :;;LX
45.
LB:;;
Y
Conclusion
MBC :;; LUTZ
BC:;; yz
•
True
(B) False
Given
46.
Conclusion
AB:;; XY
BC:;; yz
(A) True •
False i1"~ ,C-~"
'­
h
47. Use the diagram.
48. Which figures are congruent to the first
figure?
(A) I only
(B) II only
•
I and II only
(D) I, II, and III
For questions 49-50, consider MBC where AB
BC and mLA = 40° .
49. mLB +mLC = 140°
(-\
Which statement would be used to prove lines
rand s are parallel?
•
Ll and L3 are congruent
(B) L2 and L7 are complementary
(C) L 4 and Ll are congruent
(D) L8 and L6 are supplementary
•
True
(B) False
50. mLC 100°
(A) True
•
False
-----~
For questions 51-53, evaluate whether the image of
a figure under the described transformation is
congruent to the figure.
.......-
-. .
Use the Venn diagram.
Quadrilaterals
. . PaiaUdograms
51. A transformation T fo llows the rule
(x, y) ~(x+3, y). The image ofa figure
under T is congruent to the figure .
. , True
(B) False
52. A transformation T follows the rule
(x, y ) ~ (- y, - x). The image of a figure
under T is congruent to the figure.
55. A quadrilateral ABCD has 4 lines of
symmetry. Identify the area of the diagram in
whichABCD resides.
• True
(B) False
(A) III
53. A transformation T follows the rule
(x, y) ~ (x, 2y). The image ofa figure
rIj'
.
.
1 ",,'
1-
• IV
(C) V
under T is congruent to the figure.
/
i
~
.
"­
,--­
{
­
~.,
1
'
(D) VII
(A) True
•
False
mil n
In the diagram,
and p II q .
•p
-­
-­
56. Right triangle PQR has sides 0 f length 6 units,
8 units, and 10 units. The triangle is dilated by
a scale factor of 4 about point Q. What is the
area oftriangle P'Q'R,?
•q
(A) 96 square units
m
(B) 192 square units
88°
n
54. •
.-.
(D) 768 square units
XO
r
~
57. The ratio ofthe side lengths ofa triangle is
3:6:8. A second triangle is similar to the first
and its shortest side measures 8.0 centimeters.
What is the length of the longest side of the
second triangle?
What is the value of x?
(A) 44
•
88
(C) 92 (D) 176
384 square units
W YG--'«A\\ t
i
\)
.j \.;i
;r( <:. ~ Q>(\(~l\~\tl('\~' •
,
V
\
<~'f
~
(A) 3.0 cm
(B) 10.7 cm
(C) 13.0 cm
•
21.3 cm
_ 1 ~...,
61. Which figure contains two similar triangles
that are NOT congruent?
Use the diagram below.
(A)
B~--------------------------~a-·
58. What is the value of y?
(B)
(A) 13
•
18
(C) 27
In the diagram, a student has placed a mirror on
level ground, then stands so that the top of a
nearby tree is visible in the mirror.
2m
3m
36m
59. What is the height ofthe tree?
.24m
(B) 35 m
(B) 41 m
(D) 59 m
'-,:.
x
•
62. Sally constructs a triangle where two of the
angles measure 50° and 60°. Tom constructs a
triangle where two of the angles measure 50°
and 70°. What is true about the two triangles?
'5\)"
(A) The triangles cannot be similar.
(B) The triangles could be similar.
•
The triangles must
:JL~
~(J' ~
'O,J
~~S~:l~;.,,,\ !!..~""
L/
63. Triangle ABC has vertices A( -2,2),
In the diagram, JG II QR . B( -5,5), and
Q
p
7
R
60. What is the value of x?
.6
(A) 11
(C) 5
(D) 3
C(-5,3). The triangle is
dilated about the point
(1, 1)
with scale factor
4. What is the location of A'?
(A) (-8,8)
(B)
(-10,10)
• (-11,5)
(D) (-14,6)
"
1
Use the diagram.
In the diagram, segments AB and CD intersect
at E, F lies on AB , and mLAEC = 60° .
y
D
x
67. The two segments are dilated about Fwith
scale factor
64. Dilate line m about the origin with scale factor 2. What is the equation of the line's image? 60°
(C) 90°
• y=2x+4
(C) y = 4x+ 2
(D) Y
2
(A) 30°
•
(A) y=2x+ 2
~.
(D) 120°
4x+ 4
65. Which is NOT a criterion for triangle
similarity?
What is mLA'E'C'?
~; QX (X:\U Ce....
r1\
(y\ \\;;' '{
n
c~'('C\~~ 0., (,
lJ
~'.
68. In the diagram, ABCD is dilated with center 0
1
to produceA'B'C'D', and A'B' -AB.
3
(A) angle-angle
(B) angle-side-angle
(C) side-angIe-side
•
side-side
66. Y(5, 7) is the image of J(3, 3) after a dilation
with scale factor 3. Where is the center of
dilation?
(A) (-3, -9)
(B) (0,0)
• (2,1)
(D) (4,5)
•
B
OA'
What i s - ?
AA'
!
.~
(C) 2
(D) 3
(A)
3
2
- - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - -
69. Use the diagram.
---------
-
Use the right triangle. What is the value of x?
c
x
1)2 t~'2. ==\~'2.
8
B
A
~-----------~~------------~
c
72.
What is the value of x?
(A)
oJ.­
),. :;
J7
v'i6i
(A)
J;;y
•
(B)
Jb;
(D) 17
Which is equal to h?
~'\ T'I-..'1 ::. 22':::>
I~\
r­
'X. -= '1\\10\
(C) 7
erx;
(D)
73. Consider a triangle ABC. Which statement is
true?
J;;b
70. 1'(5, 7) is the image of 1(3,3) after a dilation with scale factor 3. Where is the center of dilation? (B) c
•
c
b 2 + 2abcos C
2
=a2 -
2
= a 2 +b 2 -2abcosC
2
2
2
(D) c =a +b +2abcosC
(A) (-3, -9)
(B) (0,0)
•
(2,1)
74. Use the diagram.
(D) (4,5)
A
~
71. Fred stands at comer A of a rectangular field
shown below. He needs to get to comer C.
Ar-------.B
B
9m
D
9
c
What is cos A ?
12m
c
."'"
\ -~ - A(.
What is the shortest distance from A to C?
0\2.­
(A) 9 m
(B) 13 m ~J-\nWjol(,cd'
.15m
(D) 21 m
\V,·\>\<.­
~lrL,,~
(A)
li
56
~-~
56 c?" ~
56
(B) 16
(D)
56
16
ti + C"l- - 2bCtO'::;>~
q:L ~ 1'2--\- If- _28)-('-\) to :.~) A
...... R
\\p::;' - ~Lt."'")"';,R
~\\P
_
_
~
~ :- l L£;,
75. A small airplane flies due north at 150
kilometers per hour. A wind is blowing
towards the direction 60° east of north at 50
kilometers per hour. Which figure represents
the final speed and direction of the airplane?
•
N
200 -----------1
(B) 200 N
~
N
(C) 200 ----------1
150 - '------­
150 t--------j
100
100 1-1------..,
100 t---+--~
50
50H-----l
50 t--#-------i
o
o
50 50
For questions76-78, consider a triangle ABC and
each given set of measurements.
o
N
(D) 200­
501-l--------j
o
50 50
79. The diagram shows a parallelogram ABCD.
B
~-----...,
76. AB, AC, and mLA are sufficient to solve the
triangle using the Law of Sines.
C
/p-""
(A) True
~~~ "-_ i\te.A L.Q
/,qC
•
~~
"\
B
-(
False
77. AB, AC, and mLB are sufficient to solve the
tri'tgle using the Law of Sines.
f.\
•
True
(B) False
~~'5~
f\~
AG
«:;
6
A
G
78. AB, AC, and BC are sufficient to solve the
triangle using the Law of Sines. Pi
(A) True
•
False
6
be
3
D
What is the parallelogram's area?
•
7.5../3
~ -=- 'o~
(B) 15 ~ __ l:S)\1· c..)~;;)
(C) 15../3
p.. ~ l-.~0J
(D) 30../3
84. cosko = cos(180- k)O
80. In the diagram, MBC is a non-right triangle.
C
*:.
(A) True
•
False
-~
...
,,~
C~('d ':;;
~'.f~
oW
\
I
B
c
A
85. Let cosA
(A)
1
(A) -ab 2
(B) I-m
•
~1-m2
(D)
.Jl-m
(B) absinC
•
~absinC
m. What is the value of sin A ?
rm
Which describes the area of the triangle?
2
1
2
(D) -abcosC
86. In MBC, C is a right angle, sin A =
.J7
4
What is the approximate value of cos 154°?
(B)
•
-0.90
(C)
J7
3
3
4
(D) ~
J7
Given: An angle measures kO, where k > O.
• True
(B) False
83. sinkO
J7 .
4
What is cos B?
81. Given: cos 26° "" 0.90 and sin 26° "" 0.44
sin(180-k)0
• True
(B) False
~~ec-;;
t>\
~"\(
u,"-.l.
6
~~
c
'1 )!,7. -t {:\
)('l..+-:t
",'1.::.
"
~
~'l
\'-..P
q
"'~~
to,:;>\O:;C
PI
?
clon'\
y~n
necA
-t\-\\S.
~"\
0-\
l ' '; (d (.
87. Use the diagram.
89. Use the diagram.
B
5
5J2 A
12
What is the value of d?
Which statement is true?
(A) 5
(A) sin A =~
5
•
5J2
12
.10
13
(D) 1OJ2
(B)
cosA=­
For questions 90-92, let cos XO = m.
(C) tanA= 12 5
90. cos(180 x)O =m
(A) True
88. Use the diagram.
•
B
41
A........- - - - - - L . . I I C x
Which is the value of x? (A) x
41cos35° (B) x
tan 35° 41
(C) x
41
cos35°
•
41
tan 35°
x
False
91. cos(90-x)0= m
(A) True
•
False
92. sin(90-x)0= m
•
True
(B) False
v\=\Jl_l
d= r~(~i)
d=-\O
-----
~-----
93. Let a = cos 28°. Which statement is true?
96. What is tan 60°?
(A) a = cos 62°
(A)
(B) a = cos 152°
•
J2
2
a=sin 62°
(B)
(D) a = sin 152°
13
2
(C) _1
.13
13
97. What is tan -1 (1 )?
(C) 60°
(A) 30°
(D) 90°
•
(C) 60°
95. In the diagram, BC < BD and BD = AD.
(D) 90°
c
.
A
~~----------~
4SO
98. In !1GHI , the sine of angle G equals! .
2
!1G'H'I' is a dilation of !1GHI about G with a
scale factor of 2. What is the sine of angle G'
?
D
Which statement is true?
•
cos LABC < sin LDAB
(B) cos LABC = sin LDAB
1
(A)
4
•
(C)
1
2
-
13
2
(C) cosLABC > sinLDAB
(D) 1
l
IGG
H