Transformations Cheat-Sheet

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TRANSFORMATIONS CHEAT-SHEET!
REFLECTIONS:
 Reflections are a flip.
 The flip is performed over the “line of reflection.” Lines of symmetry are examples of lines of reflection.
 Reflections are isometric, but do not preserve orientation.
Coordinate plane rules:
Over the x-axis:
(x, y)
(x, –y)
Over the y-axis:
(x, y)
(–x, y)
Over the line y = x:
(x, y)
(y, x)
Through the origin:
(x, y)
(–x, –y)
TRANSLATIONS:
 Translations are a slide or shift.
 Translations can be achieved by performing two composite reflections over parallel lines.
 Translations are isometric, and preserve orientation.
Coordinate plane rules:
(x, y)
(x ± h, y ± k) where h and k are the horizontal and vertical shifts.
Note: If movement is left, then h is negative. If movement is down, then k is negative.
DILATIONS:
 Dilations are an enlargement / shrinking.
 Dilations multiply the distance from the point of projection (point of dilation) by the scale factor.
 Dilations are not isometric, and preserve orientation only if the scale factor is positive.
Coordinate plane rules:
From the origin dilated by a factor of “c”: (x, y)
(cx, cy)
From non-origin by factor of “c”: count slope from point to projection point, multiply by “c,” count from projection point.
ROTATIONS
:
 Rotations are a turn.
 Rotations can be achieved by performing two composite reflections over intersecting lines. The resulting
rotation will be double the amount of the angle formed by the intersecting lines.
 Rotations are isometric, and do not preserve orientation unless the rotation is 360
o
or exhibit rotational
symmetry back onto itself.
 Rotations of 180
o
are equivalent to a reflection through the origin.
Coordinate plane rules:
Counter-clockwise:
Clockwise:
Rule:
o
o
90
270
(x, y)
(–y, x)
o
o
180
180
(x, y)
(–x, –y)
o
o
270
90
(x, y)
(y, –x)

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