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!

Reflections

1. 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)

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 2,4

A 0, 8

T 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 1,2

A 3, 5

T 4, 1

H' 1,2

A ' 3, 5

T' 4, 1