1. Reflecting over the x-axis and y-axis
Coordinate Reflections - 1
Reflecting over the x-axis and y-axis

2. FLIP IT OVER! Original shape Reflected shape Mirror line
3 squares from mirror line
3 squares from mirror line
FLIP IT OVER!
Original shape
Reflected shape
Mirror line
Make sure the reflected shape is the same distance from the mirror line as the original shape

3. E E 3 squares from mirror line 3 squares from mirror line
FLIP IT OVER!
Original shape
Reflected shape
Mirror line
Make sure the reflected shape is the same distance from the mirror line as the original shape

4. Reflections
pre-image and image are equidistant from the line of reflection
2. the line of reflection is the perpendicular bisector of
the segment connecting two reflected points
3. Orientation of the image of a polygon reflected is
opposite the orientation of the pre-image
(orientation – CW: clockwise;
CCW: Counter-clockwise)

5. Reflection RULES

6. Reflect across the x-axis
Change the sign of the y-value

7. Reflect the object below over the x-axis:
Name the coordinates of the original object: A
A: (-5, 8)
B: (-6, 2) D C
C: (6, 5)
D: (-2, 4) B
Name the coordinates of the reflected object:
A’: (-5, -8) B’
B’: (-6, -2) D’
C’: (6, -5) C’
D’: (-2, -4) A’
The x-coordinates same; the y-coordinates  opposite.

8. Quadrilateral ABCD.
Graph ABCD and its image under reflection in the x-axis.
Use the vertical grid lines to find the corresponding point for each vertex so that the x-axis is equidistant from each vertex and its image. D'
A(1, 1)  A' (1, –1) C'
B(3, 2)  B' (3, –2)
C(4, –1)  C' (4, 1)
D(2, –3)  D' (2, 3) A' B'
The x-coordinates stay the same, but the y-coordinates are opposite.
That is, (x, y)  (x, –y).

9. Reflect across the x-axis

10. Reflect across the y-axis
Change the sign of the x-value

11. Reflect the object below over the y-axis:
Name the coordinates of the original object: T T’
T: (9, 8)
R: (9, 3)
Y: (1, 1) R’ R
Name the coordinates of the reflected object: Y’ Y
T’: (-9, 8)
R’: (-9, 3)
Y’: (-1, 1)
The x-coordinates  opposite, the y-coordinates  same

12. B' A' C' D' The x-coordinates are opposite, but the
Quadrilateral ABCD has vertices
Graph ABCD and its image under reflection in the y-axis.
Use the horizontal grid lines to find the corresponding point for each vertex so that the y-axis is equidistant from each vertex and its image. B'
A(1, 1)  A' (–1, 1) A'
B(3, 2)  B' (–3, 2)
C(4, –1)  C' (–4, –1)
D(2, –3)  D' (–2, –3) C' D'
The x-coordinates are opposite, but the
y-coordinates stay the same.
That is, (x, y)  (–x, y).

13. Reflect across the y-axis