REFLECTING OVER THE X-AXIS AND Y-AXIS

Coordinate Reflections - 1

Mirror line

Original shape Reflected shape

Make sure the reflected shape is the same distance from the mirror line as the original shape

3 squares from mirror line

3 squares from mirror line

FLIP IT OVER!

Mirror line

Original shape Reflected shape

Make sure the reflected shape is the same distance from the mirror line as the original shape

3 squares from mirror line

3 squares from mirror line

FLIP IT OVER!

Reflections1. pre-image and image are equidistant from the line of

reflection2. the line of reflection is the perpendicular bisector of the segment connecting two reflected points3. Orientation of the image of a polygon reflected is opposite the orientation of the pre-image

(orientation – CW: clockwise; CCW: Counter-clockwise)

Reflection RULES

Reflect across the x-axis

x,y x, y Change the sign of the y-value

Reflect the object below over the x-axis:Name the coordinates of the original object:

A

B

CD

A: (-5, 8)

B: (-6, 2)

C: (6, 5)

D: (-2, 4)

A’

B’

C’D’

Name the coordinates of the reflected object:

A’: (-5, -8)

B’: (-6, -2)

C’: (6, -5)

D’: (-2, -4)

The x-coordinates same; the y-coordinates opposite.

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.

A(1, 1) A' (1, –1)

B(3, 2) B' (3, –2)C(4, –1) C' (4, 1)

D(2, –3) D' (2, 3)

The x-coordinates stay the same, but the y-coordinates are opposite.

That is, (x, y) (x, –y).

A' B'

C'

D'

Reflect across the x-axis

C 2,4A 0, 8T 3,5

C ' 2, 4 A ' 0,8 T' 3, 5

Reflect across the y-axis

x,y x,y Change the sign of the x-value

Reflect the object below over the y-axis:Name the coordinates of the original object:

Y

R

TT: (9, 8)

R: (9, 3)

Y: (1, 1)

R’

T’

Y’Name the coordinates of the reflected object:

T’: (-9, 8)

R’: (-9, 3)

Y’: (-1, 1)

The x-coordinates opposite, the y-coordinates same

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.

A(1, 1) A' (–1, 1)B(3, 2) B' (–3, 2)

C(4, –1) C' (–4, –1)D(2, –3) D' (–2, –3)

The x-coordinates are opposite, but the y-coordinates stay the same.

That is, (x, y) (–x, y).

A'B'

C'

D'

Reflect across the y-axis

H 1,2A 3, 5T 4, 1

H' 1,2 A ' 3, 5 T' 4, 1