1. Introduction and Review Information

2. Example
Pre-Image
Image A' A B B' C' C

3. Remember equations for horizontal lines:
Writing Equations
Remember equations for horizontal lines:
y = 2 is horizontal line crossing y-axis at 2
y = –4 is horizontal line crossing y-axis at 4
y=2
y =–4

4. Remember equations for vertical lines:
Writing Equations
Remember equations for vertical lines:
x = 2 is vertical line crossing x-axis at 2
x = –4 is vertical line crossing x-axis at –4
x=2
x =–4

5. 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

6. Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line.

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..

9. 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 C' D'
Step 3 – Go that same distance
on the other side of line
Step 4 – LABEL THE NEW POINTS
Step 5 – Continue with other points

10. Reflecting across y-axis
Pre-image Image
C'(3, 7) C A T C’
C(-3, 7)
A(-3, 2)
A'(3, 2) A’ T’
T(2, 2)
T'(-2, 2)
What do you notice about
the x and y coordinates
of the pre-image and image
points?

11. Reflecting across x-axis
Reflect the following shape across the x-axis
Pre-image Image
M(2, 1)
M’(2, -1)
A(-1, 1)
A’(-1, -1) T H
T(-3, 5)
T’(-3, -5) A M
H(4, 5)
H’(4, -5) A’ M’ T’ H’
What do you notice about
the x and y coordinates
of the pre-image and image
points?

12. Reflecting across the line y = x
Pre-Image Image
F(-3, 0)
F‘(0, -3)
I(4, 0) I’ S’
I'(0, 4)
S(4, -9) F I
S'(-9, 4) F’
H(-3, -9)
H'(-9, -3) H’
What do you notice about
the x and y coordinates
of the pre-image and image
points? H S

14. 8. Reflect across y = –x M(-5, 2) O(-2, 2) V(0, 6) E(-7, 6)

15. 8. Reflect across y = -3
H’(-12, 2)
A’(7, -7)
T’(2, -7) H T A

16. 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.