Reflections in the y-axis

Change the sign of the x-coordinate. (x,y)-> (-x,y)

Reflection in the x-axis

Change the sign of the y-coordinate. (x,y)-> (x,-y)

y=x

(x,Y)-> (y,x)

Properties of Reflection

Size is not changed. Shape is not changed. Orientation is changed.

Vertical Translation

Add b units to the y-coordinate. In the figure at the right. (x,y) -> (x, y+b)

Horizontal translation

Add a units to the x-coordinate. (x,y)-> (x+a, y)

Properties of Translation

The size, shape, and orientation of a figure are not changed after translation. Only the position of a figure is changed after translation. After translation, the original figure and its image are congruent.

Rotation of 90° Clockwise

To rotate a point, first change the sign of the x-coordinate. Then switch the x and y-coordinates. (x, y)-> (y,-x)

Rotation of 90° Counterclockwise

To rotate a point, first change the sign of the y-coordinate, Then switch the x and y-coordinates. (x,y)-> (-y, x)

Rotation of 180°

To rotate a point, change the sign of both the x and y- coordinates. (x,y) -> (-x,-Y)

Properties of Rotation

The size,shape, and orientation of a figure are not changed after a rotation. After a rotation, a figure and its image are congruent.

Dilation Centered at (0,0)

Multiply both the x and y-coordinates by a positive number k, or scale factored. (x,y)->(kx,ky)

Properties of Dilation

A figure and its image are similar. This means that the corresponding sides are proportional. The orientation of a figure is not changed under dilation. The shape after dilation is the same but the size is different.