1. A transformation is a change in the position, size, or
shape of a figure or graph. It is sometimes called a
mapping.
Examples of transformations are:
translations, reflections, rotations, and dilations.

2. Preimage:
the original figure
Image:
the figure after the transformation

3. Which of the transformations are examples of
Isometry:
a transformation that does not change the size or shape of a figure
Which of the transformations are examples of
isometry?
Translations, reflections, and rotations

4. Reflections 12-1 I CAN - Accurately reflect a figure in space.
- Reflect a figure across the x-axis, the y-axis
the line y = x, or the line y = –x
Holt Geometry

5. Reflection:
Reflection is a transformation that moves a figure by flipping it across a line

6. Reflection
The original figure is called the preimage and the reflected figure is called the image.
A reflection is the reflected image always congruent to the preimage?
What do we call this?

7. Example 1: Identifying Reflections
Tell whether each transformation appears to be a reflection. Explain. A. B.
No; the image does not
Appear to be flipped.
Yes; the image appears to be flipped across a line.

8. Check It Out! Example 1
Tell whether each transformation appears to be a reflection. a. b.
No; the figure does not appear to be flipped.
Yes; the image appears to be flipped across a line.

9. We are going to reflect images on the coordinate plane across given lines 

11. Reflecting across vertical lines (x = a)
Reflect across x = -2
Step 1 – Draw line of reflection A B B' A'
Step 2 – Pick a starting point,
count over-ALWAYS vertically
or horizontally to line D C D' C'
Step 3 – Go that same distance
on the other side of line
Step 4 – LABEL THE NEW POINTS
Step 5 – Continue with other points
Do # 3 on your worksheet
Label the coordinates of the preimage.

12. Reflecting across y-axis
Reflect the following shape across the y-axis
Pre-image Image
A'( , )
A( , ) A
B( , )
B'( , ) B
C( , )
C'( , ) C
Do # 4 on your worksheet
Label the coordinates of the preimage.

13. Reflecting across x-axis
Reflect the following shape across the x-axis
Pre-image Image
A'( , ) A
A( , )
B( , )
B'( , ) B C
C( , )
C'( , )
Do #5 on your worksheet
Label the coordinates of
the preimage.

14. F'( , ) I'( , ) S'( , ) H'( , ) Reflecting across the line y = x
Remember:
Move ONLY vertically or horizontally…think about why?
Pre-Image Image
F( , )
F'( , )
I( , )
I'( , ) F I
S( , )
S'( , )
H( , )
H'( , ) H S
Do #6 on your worksheet
Label the coordinates of
the preimage.

15. Look back at the problems you just completed.
Compare the x and y-coordinates for the pre-image and image.
Can you see a rule for each reflection?

17. Reflect the rectangle with vertices S(3, 4),
Check It Out!
Reflect the rectangle with vertices S(3, 4),
T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis.
The reflection of (x, y) is (x,–y).
S(3, 4) S’(3, –4) V S U T
T(3, 1) T’(3, –1)
U(–2, 1) U’(–2, –1) V’ S’ U’ T’
V(–2, 4) V’(–2, –4)
Graph the image and preimage.

18. Reflect across y = –x C’( , ) A’( , ) K’( , ) E’( , )
Do #8 on your worksheet

19. Reflect the figure with the given vertices across the given line.
Lesson Quiz
Reflect the figure with the given vertices across the given line.
1. A(2, 3), B(–1, 5), C(4,–1); y = x
A’(3, 2), B’(5,–1), C’(–1, 4)
2. U(–8, 2), V(–3, –1), W(3, 3); y-axis
U’(8, 2), V’(3, –1), W’(–3, 3)
3. E(–3, –2), F(6, –4), G(–2, 1); x-axis
E’(–3, 2), F’(6, 4), G’(–2, –1)