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Math A Lab – Transformational Geometry
Part A
What is the image of point 2,5  under the translation that shifts  x, y  to x  3, y  2  ?
What is the image of point 4,7  under the
translation that shifts  x, y  to x  1, y  4 ?
What is the image of point 3,2  under the
translation that shifts  x, y  to x  1, y  5 ?
Part B
State which transformation of ABC to A' B' C ' is shown in the accompanying diagram.
State which transformation of ABC to
A' B' C ' is shown in the accompanying
diagram.
State which transformation of ABC to
A' B' C ' is shown in the accompanying
diagram.
Part C
When the point 2,5 is reflected in the x-axis, what are the coordinates of its image?
When the point 6,3 is reflected in the y-axis,
what are the coordinates of its image?
When the point  1,4  is reflected in the line
y  x , what are the coordinates of its image?
Part D
How many line symmetries does the following figure have?
How many line symmetries does the following
figure have?
How many line symmetries does the following
figure have?
Part E
(True or False) A Translation always produces an image that is congruent to the original figure.
(True or False) A Dilation always produces an
image that is congruent to the original figure.
(True or False) A Reflection always produces
an image that is congruent to the original figure.
Part F
Helen is using a capital H in an art design. How many line symmetries and point symmetries does the
H have?
Lines of symmetry
Points of symmetry
Helen is using a capital S in an art design. How
many line symmetries and point symmetries
does the S have?
Helen is using a capital X in an art design. How
many line symmetries and point symmetries
does the X have?
Lines of symmetry
Lines of symmetry
Points of symmetry
Points of symmetry
Part G
Which of the following have point symmetry?
M
A T
H
Which of the following have point symmetry?
W
O N B
Which of the following have point symmetry?
Z E D S
PART H
In the accompanying diagram, ABC is congruent to A' B' C ' . Which transformation is represented
by A' B' C ' ?
In the accompanying diagram, ABC is
congruent to A' B' C ' . Which transformation is
represented by A' B' C ' ?
In the accompanying diagram, ABC is similar
but not congruent to A' B' C ' . Which
transformation is represented by A' B' C ' ?
PART I
If x  2 and y  1 , which point on the accompanying set of axes represents the translation
x, y   x  2, y  3 ?
If x  2 and y  1 , which point on the set of
axes above represents the translation
x, y   x  2, y  3 ?
If x  2 and y  1 , which point on the set of
axes above represents the translation
x, y   x  2, y  3 ?
PART J
The accompanying diagram shows a transformation. Which transformation performed on figure 1
resulted in figure 2?
The accompanying diagram shows a
transformation. Which transformation
performed on figure 1 resulted in figure 2?
The accompanying diagram shows a
transformation. Which transformation
performed on figure 1 resulted in figure 2?
PART K
In the accompanying diagram, which transformation changes the solid-line parabola to the dotted-line
parabola?
In the accompanying diagram, which
transformation changes the solid-line parabola to
the dotted-line parabola?
In the accompanying diagram, which
transformation changes the solid-line parabola to
the dotted-line parabola?
PART L
Draw all the symmetry lines on the accompanying figure.
Draw all the symmetry lines on the
accompanying figure.
Draw all the symmetry lines on the
accompanying figure.
PART M
The coordinates of the endpoints of AB are A (0,6) and B (4,6) . Graph and state the coordinates of
A’ and B’, the image of A and B after AB is reflected in the x-axis.
The coordinates of the endpoints of AB are
A (1,2) and B (5,7) . Graph and state the
coordinates of A’ and B’, the image of A and B
after AB is reflected in the y-axis.
The coordinates of the endpoints of AB are
A (0,4) and B (1,6) . Graph and state the
coordinates of A’ and B’, the image of A and B
after AB is reflected in the line y  x .
PART N
The coordinates of the endpoints of AB are A 2,6  and B 4,2  . Is the image A' ' B' ' the same if it is
reflected in the x-axis, then dilated by 1 2 as the image is if it is dilated by 1 2 , then reflected in the xaxis? Justify your answer.
The coordinates of the endpoints of AB are
A 3,5  and B 1,2 . Is the image A' ' B' ' the same
if it is reflected in the y-axis, then dilated by 2 as
the image is if it is dilated by 2, then reflected in
the x-axis? Justify your answer.
The coordinates of the endpoints of AB are
A 0,4  and B 2,6  . Is the image A' ' B' ' the
same if it is reflected in the y-axis, then dilated
by 1 2 as the image is if it is dilated by 1 2 , then
reflected in the x-axis? Justify your answer.
PART O
On the accompanying set of axes, graph ABC with coordinates A  1,2  , B 0,6  , and C 5,4  . Then
graph A' B' C ' , the image of ABC after a dilation of 2.
On a sheet of graph paper,, graph ABC with
coordinates A  3,2 , B 0,4  , and C 6,3 .
Then graph A' B' C ' , the image of ABC after
a translation x, y   x  3, y  2
On a sheet of graph paper, graph ABC with
coordinates A  1,2  , B 0,6  ,
and C 5,4  . Then graph A' B' C ' , the image of
ABC after a rotation of 90 degrees about the
origin counterclockwise.
PART P
Triangle SUN has coordinates S 0,6  , U 3,5  , and N 3,0  . On the accompanying grid, draw and
label SUN . Then, graph and state the coordinates of S' U' N' , the image of SUN after a
reflection in the y-axis.
Triangle XYZ has coordinates X  2,5 ,
Y 4,2  , and Z  1,4  . On a sheet of graph
paper, draw and label XYZ . Then, graph and
state the coordinates of X ' Y' Z' , the image of
XYZ after a reflection in the x-axis.
Triangle ABC has coordinates A 0,6  , B 3,5  ,
and C 3,0  . On a sheet of graph paper, draw
and label ABC . Then, graph and state the
coordinates of A' B' C' , the image of ABC
after a reflection in the line y  x .
PART Q
On the accompanying grid, draw and label quadrilateral ABCD with points A 1,2 , B 6,1 , C 7,6  ,
and D 3,7  . On the same set of axes, plot and label quadrilateral A’B’C’D’, the reflection of
quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A’B’C’D’.
On a sheet of graph paper, draw and label
quadrilateral QRST with points Q 1,1 , R 3,5  ,
S 9,5  , and T 7,1 . On the same set of axes,
plot and label quadrilateral Q’R’S’T’, the
reflection of quadrilateral QRST in the x-axis.
Determine the area, in square units, of
quadrilateral Q’R’S’T’.
On a sheet of graph paper, draw and label
quadrilateral MATH with points M  3,2  ,
A 0,3 , T 2,1 , and H  4,1 . On the same set
of axes, plot and label quadrilateral M’A’T’H’,
the reflection of quadrilateral MATH in the yaxis. Determine the area, in square units, of
quadrilateral M’A’T’H’.