13 terms

# Transformations

Includes Reflections, Translations, Rotations and Dialations
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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.