Translations
Lesson 9-8
Translations


Translations are used on the coordinate
plane.
A translation is a shift or movement of a
figure a given number of places on the
coordinate plane.
EXAMPLE
A
C
B
D
Suppose we have parallelogram
ABCD as shown on the graph.
We can “translate” this shape
5 units to the right and 3 units
down. The new image would
look like this:
A
Notice that the entire new image
Is shifted 5 units to the right and
3 units down. The labels of the
image are noted with a prime ‘
symbol.
B
A’
C
B’
D
C’
D’
TRY THIS
Translate triangle QRS 4 units to
The left and 5 units up.
Q
R
S
TRY THIS
Q’
Translate triangle QRS 4 units to
The left and 5 units up.
R’
Q
S’
R
S
Symmetry and Reflections
Lesson 9-9



Reflection is a mirror image of a figure.
In geometry, reflectional symmetry
occurs when one half of a figure is a
mirror image of the other half.
The line of symmetry is the line that
divides a figure into two congruent
halves.
Symmetry

Notice that one half of the pentagon is
the mirror image of the other.
Line of symmetry
Try This

Which of the following figures have
reflectional symmetry?
Try This

Which of the following figures have
reflectional symmetry?
YES
YES
YES
NO
YES
Symmetry

Many figures have more than one line
of symmetry. Notice that the square
has 4 lines of symmetry.
Try This

Draw all the lines of symmetry for the
following figures.
Try This

Draw all the lines of symmetry for the
following figures.
Try This

Draw all the lines of symmetry for the
following figures.
Try This

Draw all the lines of symmetry for the
following figures.
Try This

Draw all the lines of symmetry for the
following figures.
Try This

Draw all the lines of symmetry for the
following figures.
Reflections


Reflections can also be used on the
coordinate plane.
A reflection is a figure that has been
flipped over a line of reflection.
EXAMPLE
A
B
Suppose that line segment AB is
graphed as shown. If it is reflected
over the y-axis, it would look like this:
EXAMPLE
A
B
Notice that the image of the line
segment is a mirror image of the
original one. It is as if the paper
were folded on the y-axis and it
left an identical imprint on the
other side of the axis.
A’
B’
Try This
Graph the image of triangle DEF
after a reflection over the x-axis.
D
E
F
Try This
D
E
F
F’
E’
D’
Try This
Now graph the image of
parallelogram ABCD after it is
reflected over x = 2
A
C
B
D
Try This
Line of reflection
A
C
B
D
Notice that the line of
reflection is x = 2. It is as
if the paper were folded on
the line x = 2.
B’
A’
D’
C’