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Review of Transformations - Jr. level
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A quick review of transformations in the coordinate plane.

Line Reflections


Remember that a reflection is simply a flip.  Under a reflection, the figure does not change size (it is a rigid transformation). 

It is simply flipped over the line of reflection. 
The orientation (lettering of the diagram) is reversed.
 

line reflection in x-axisrefX1

Reflection in the x-axis:  

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. 
i2    or     i3

Reflection in the y-axis:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite. 
i4    or     i5

Reflection in y = x:

When you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places. 
i6      or      i7

Reflection in y = -x:

When you reflect a point across the line y = -x, the x-coordinate and the y-coordinate change places and are negated (the signs are changed). 
i8   or     i9

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Point Reflections

A point reflection exists when a figure is built around a single point called the center of the
figure. 

For every point in the figure, there is another point found directly opposite it on the
other side of the center. 

The figure does not change size (it is a rigid transformation).
 

point reflection in originrefX1
Reflection in the Origin:
While any point in the coordinate plane may be used as a point of reflection, the most commonly used point is the origin.
i22    or    i23


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Rotations

A rotation turns a figure through an angle about a fixed point called the center.
The most popular center of rotation is the origin, but may be other points.
 
A positive angle of rotation turns the figure counterclockwise, and a negative angle of rotation turns the figure in a clockwise direction

The figure does not change size (it is a rigid transformation).

rotation 90º counterclockwise centered at originrefX1

Rotations on the coordinate axes are assumed to be counterclockwise (CCW),
unless otherwise stated.

Rotation of 90º: (CCW)
   rn1
Rotation of 180º: (CCW)
  rn2 (same as reflection in origin)
Rotation of 270º: (CCW)
  rn3

If a problem specifically asks for a clockwise (CW) rotation on the axes,
the formulas stated above for 90º and 270º will not work.
Instead, you will need: (for clockwise only) 90cw and 270 cw
.
The formula for a rotation of 180º is the same in both directions. dividerdash


Dilations

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size (the figures are similar). 

The description of a dilation includes the scale factor and the center of the dilation.  

A dilation "enlarges" or "reduces" a figure (it is not a rigid transformation).
 

dilation of scale factor 2 centered at the origin.dilX1

Dilation of scale factor k:

The center of a dilation is most often the origin, O. It may however, be some other point in the coordinate plane which will be specified.
dorigin


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Translations

A translation "slides" an object a fixed distance in a given direction. 

The original object and its translation have the same shape and size (it is a rigid transformation), and they face in the same direction. 

translation 6 units left and 3 units up.dilX1

Translation of  h, k:

  i28
If h > 0, the original object is shifted h units to the right.
If h < 0, the original object is shifted | h | units to the left.
If k > 0, the original object is shifted k units up.
If k < 0, the original object is shifted | k | units down.


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