Graphing & Describing
“Reflections”
We have learned that there are 4 types of transformations:
1)
2)
3)
4)
Translations
Reflections
Rotations
Dilations
The first 3 transformations preserve the size and shape of the figure.
In other words…
• If your pre-image (the before) is a trapezoid,
your image (the after) is a congruent trapezoid.
• If your pre-image contains parallel lines,
your image contains congruent parallel lines .
• If your pre-image is an angle,
your image is an angle with the same measure.
Yesterday… our lesson was
ALL about translations.
Today… our lesson will focus
on reflections.
Let’s Get Started
Section 1: Comparing a translation
to a reflection.
Section 2: Performing a reflection over the
x- or y-axis.
Section 3: Performing a reflection over a line.
Section 4: Describing a reflection.
Turn and Discuss
 Which of the below is the translation and which is the
reflection. Be ready to explain how you know to the class.
#1
#2
Turn and Discuss
 Which of the below is the translation and which is the
reflection. Be ready to explain how you know to the class.
#1
#2
If You Remember…
 A translation is a slide that moves a figure to a different
position (left, right, up or down) without changing its size or
shape and without flipping or turning it.
You can use a slide arrow to
show the direction and
distance of the movement.
A reflection (flip) creates a
mirror image of a figure.
Moving On
Section 1: Comparing a translation
to a reflection.
Section 2: Performing a reflection over the
x- or y-axis.
Section 3: Performing a reflection over a line.
Section 4: Describing a reflection.
A Reflection is a Flip over a Line
A reflection is a flip because the figure is “flipped” over
a line. Each point in the image is the same distance from
the line as the original point.
t
A'
A
B
C
C'
B'
A and A' are both 6 units from line t.
B and B' are both 6 units from line t.
C and C' are both 3 units from line t.
Each vertex in ∆ABC is the same
distance from line t as the vertices in
∆A'B'C'.
Check to see if the pre-image and image are congruent.
STEPS and EXAMPLE
Reflect the figure across the y-axis.
Step 1: Start with any
vertex and count the number
of units to the specified axis
(or line).
Step 2: Measure the same
distance on the other side of
the axis (or line) and place a
dot. Label using prime
notation.
Step 3: Repeat for the
other vertices.
Check to see if the pre-image and image are congruent.
Reflection Across the Y-AXIS
Let’s name the coordinates of each figure.
reflection
across y-axis
Pre-image
Image
A(
,
)
A' (
,
)
B(
,
)
B' (
,
)
C(
,
)
C' (
,
)
D(
,
)
D' (
,
)
----- When you reflect across the y-axis -----
Compare the coordinates of
the pre-image
to the
image.
The y-coordinate
will always
stay
the same.
The x-coordinate will always flip signs.
What do you notice?
𝑥, 𝑦
→
−𝑥, 𝑦
Let’s take a look at the same pre-image and
see what it looks like after being reflected
across the x-axis …
Reflection Across the X-AXIS
Here is the same pre-image but this time it is reflected across the x-axis.
Pre-image Image
reflection
across x-axis
𝐀 (−𝟔, 𝟓)
𝐀′ (−𝟔, −𝟓)
𝐁 (−𝟑, 𝟓)
𝐁′ (−𝟑, −𝟓)
𝐂 (−𝟑, 𝟏)
𝐂′ (−𝟑, −𝟏)
𝐃 (−𝟔, 𝟑)
𝐃′ (−𝟔, −𝟑)
------ When
you reflect
the x-axis
Compare
the across
coordinates
of -----the pre-image
to the
The x-coordinate
will always
stayimage.
the same.
The y-coordinate will always flip signs.
What do you notice?
𝒙, 𝒚
→
𝒙, − 𝒚
Reflect ∆𝑨𝑩𝑪 across the y-axis.
Name the coordinates
of your reflection:
You Try #1
Reflect figure QRST across the x-axis
Name the coordinates
of your reflection:
You Try #2
Turn and Discuss
 Which could be a point reflected across the x-axis?
 Which could be a point reflected across the y-axis?
Be prepared to explain how you know to the class.
A. 𝟓, 𝟖 → (−𝟓, −𝟖)
B. 𝟓, 𝟖 → (𝟓, −𝟖)
C. 𝟓, 𝟖 → (−𝟓, 𝟖)
Moving On
Section 1: Comparing a translation
to a reflection.
Section 2: Performing a reflection over the
x or y-axis.
Section 3: Performing a reflection over a line.
Section 4: Describing a reflection.
Reflections Across a Vertical or Horizontal Line
 You may be asked to reflect a figure across a
line that is not the x-axis or the y-axis.
 Let’s see how to do that…
Example over a Vertical Line
line of reflection
First, draw the
line of reflection.
Then follow the
normal steps for
reflecting over a
line.
Example over a Horizontal Line
First, draw the
line of reflection.
line of reflection
Then follow the
normal steps for
reflecting over a
line.
Reflect ∆𝑬𝑭𝑮 across the line 𝒙 = 𝟐
Name the coordinates
of your reflection:
You Try #3
Reflect figure ABCD across the line 𝐲 = 𝟒
Name the coordinates
of your reflection:
You Try #4
Moving On
Section 1: Comparing a translation
to a reflection.
Section 2: Performing a reflection over the
x or y-axis.
Section 3: Performing a reflection over a line.
Section 4: Describing a reflection.
Describing a Reflection
 In this Section, you will be given a reflection that has
already been performed, and you will describe what
occurred.
 Example:
Description
reflection across
𝒙 = −𝟏
You Try
Describe the below reflections.
5)
6)
You Try
7)
Which of the following represents a single
reflection of Figure 1?
Figure 1
A
C
B
D
You Try
8)
Describe the reflection below.
A) across the y-axis
B) across the x-axis
C) across the line y=-3
D) across the line x=4
You Try
9)
Describe the below reflection of point (3,-7).
𝟑, −𝟕 → (−𝟑, −𝟕)
A.
B.
reflection across the x-axis
reflection across the y-axis
Questions
1)
What is the difference between a translation and a reflection?
2)
How do you perform a reflection?
3)
Will a reflection ALWAYS result in a congruent figure?
4)
How would you complete this if it was a reflection over the
x-axis?
(9, 3) → ( , )
5)
How would you complete this if it was a reflection over the
y-axis?
(9, 3) → ( , )
6)
How do “describe” a reflection?
END OF POWERPOINT