1. Reflections
Lesson 3.4.1

2. Reflections 3.4.1 California Standard: What it means for you:
Lesson
3.4.1
Reflections
California Standard:
Measurement and Geometry 3.2
Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
What it means for you:
You’ll learn what it means to reflect a shape. You’ll also see how to draw and describe reflections.
Key words:
reflection
image
flip
prime
coordinates
x-axis/y-axis

3. Reflections 3.4.1 The next few Lessons are about transformations.
A transformation is a way of changing a shape.
For example, it could be flipping, stretching, moving, enlarging, or shrinking the shape.
The first type of transformation you’re going to meet is reflection.

4. Reflections 3.4.1 A Reflection Flips a Figure Across a Line
Lesson
3.4.1
Reflections
A Reflection Flips a Figure Across a Line
A reflection takes a shape and makes a mirror image of it on the other side of a given line. A B C A' C' B'
Here triangle ABC has been reflected or “flipped” across the line of reflection.
A' is read as “A prime.”
The reflections of points A, B, and C are labeled A', B', and C'.
The whole reflected triangle A'B'C' is called the image of ABC.

5. Reflections 3.4.1 Reflect triangle DEF across the y-axis. Solution
Lesson
3.4.1
Reflections
Example 1
7 units
7 units
Reflect triangle DEF across the y-axis. y 6 E D D' 4 2 F x –8 –6 –4 –2 2 4 6 8
Solution
Step 1: Pick a point to reflect — point D.
Point D is 7 units away from the y-axis.
Move across the y-axis and find the point 7 units away on the other side. This is where you plot the point D'.
Solution continues…
Solution follows…

6. Reflections 3.4.1 Reflect triangle DEF across the y-axis.
Lesson
3.4.1
Reflections
Example 1
Reflect triangle DEF across the y-axis. y 6 E E' D D' 4 2 F F' x –8 –6 –4 –2 2 4 6 8
Solution (continued)
Step 2: Repeat step 1 for points E and F.
Step 3: Join the points to complete triangle D'E'F'.

7. Reflections 3.4.1 Guided Practice
Lesson
3.4.1
Reflections
Guided Practice
In Exercises 1–2, copy each shape onto a set of axes, then draw its reflections across the y-axis and the x-axis. –6 –4 –2 2 4 6 y x –6 –4 –2 2 4 6 y x R' S' T' R S T L' K' N' M' K L M N
N''
M''
K''
L''
T''
S''
R''
Solution follows…

8. Reflections 3.4.1 Guided Practice
Lesson
3.4.1
Reflections
Guided Practice
In Exercises 3–4, copy each shape onto a set of axes, then draw its reflections across the y-axis and the x-axis. –6 –4 –2 2 4 6 y x –6 –4 –2 2 4 6 y x
W''
X''
Y''
Z''
I''
G''
H'' G H I' G' H' W' X' Y' Z' W Z X I Y
Solution follows…

9. Reflections 3.4.1 Reflections Change Coordinate Signs D (–7, 4)
Lesson
3.4.1
Reflections
Reflections Change Coordinate Signs
A reflection across the x-axis changes (x, y) to (x, –y). A reflection across the y-axis changes (x, y) to (–x, y).
To see this, look again at the reflection from Example 1. The coordinates of the corners of the triangles are shown. –8 –6 –4 –2 2 4 6 8 y x D E F D' E' F'
D (–7, 4)
E (–2, 5)
F (–3, 2)
D' (7, 4)
E' (2, 5)
F' (3, 2)
When DEF is reflected across the y-axis, the y-coordinate stays the same and the x-coordinate changes from negative to positive.

10. Lesson
3.4.1
Reflections
If you reflect DEF across the x-axis, the x-coordinate stays the same and the y-coordinate changes from positive to negative. –8 –6 –4 –2 2 4 6 x D E F
D"
E"
F" y
D (–7, 4)
E (–2, 5)
F (–3, 2)
D'' (–7, –4)
E'' (–2, –5)
F'' (–3, –2)
When you’re drawing more than one image, the first should be called A' B' C', the second is A'' B'' C'' and so on.

11. Reflections 3.4.1 Guided Practice
Lesson
3.4.1
Reflections
Guided Practice
In Exercises 5–8, give the coordinates of the image produced.
5. A: (5, 2), (4, 7), (6, 1). Triangle A is reflected over the x-axis.
6. B: (9, 9), (–4, 8), (–2, 6). Triangle B is reflected over the y-axis.
7. C: (–2, 10), (2, 10), (5, 5), (0, –3), (–5, 5). Pentagon C is reflected over the x-axis.
8. Pentagon C from Exercise 7 is reflected over the y-axis.
(5, –2), (4, –7), (6, –1)
(–9, 9), (4, 8), (2, 6)
(–2, –10), (2, –10), (5, –5), (0, 3), (–5, –5)
(2, 10), (–2, 10), (–5, 5), (0, –3), (5, 5)
Solution follows…

12. Reflections 3.4.1 Guided Practice
Lesson
3.4.1
Reflections
Guided Practice
Exercises 9–11 give the coordinates of the corners of a figure and its reflected image. Describe each reflection in words.
9. D: (5, 2), (6, 3), (8, 1), (4, 1); D': (5, –2), (6, –3), (8, –1), (4, –1)
10. E: (–6, –1), (–3, –6), (–9, –4); E': (6, –1), (3, –6), (9, –4)
11. F: (0, 0), (0, 5), (3, 3); F': (0, 0), (0, 5), (–3, 3)
Reflection over x-axis
Reflection over y-axis
Reflection over y-axis
Solution follows…

13. Reflections 3.4.1 Independent Practice
Lesson
3.4.1
Reflections
Independent Practice
Copy the grid and figures shown below, then draw the reflections described in Exercises 1–3.
1. Reflect A across the x-axis. Label the image A'.
2. Reflect A across the y-axis. Label the image A''.
3. Reflect B across the x-axis. Label the image B'.
–10 –5 5 10 y x
A'' A A' B' B
Solution follows…

14. Reflections 3.4.1 Independent Practice
Lesson
3.4.1
Reflections
Independent Practice
Copy the grid and figures shown below, then draw the reflections described in Exercises 4–6.
4. Reflect B across the y-axis. Label the image B''.
5. Reflect C across the x-axis. Label the image C'.
6. Reflect C across the y-axis. Label the image C''.
–10 –5 5 10 y x
B''
C'' C C' B
Solution follows…

15. Reflections 3.4.1 Independent Practice
Lesson
3.4.1
Reflections
Independent Practice
In Exercises 7–8, copy the figures onto graph paper and reflect each one over the line of reflection shown.
Solution follows…

16. Reflections 3.4.1 Independent Practice
Lesson
3.4.1
Reflections
Independent Practice
In Exercise 9, copy the figure onto graph paper and reflect it over the line of reflection shown. 9.
Solution follows…

17. Lesson
3.4.1
Reflections
Round Up
Don’t forget that a reflection makes a back-to-front image — like the image you see when you look in a mirror.
Unless the original is symmetrical, the image shouldn’t be the same way around as the original. If it is the same way around, that’s a translation, not a reflection.
You’ll learn about translations in the next Lesson.