Transformations notes Flashcards
Reflections are a
flip or mirror image
The flip is performed over the “line of reflection.” Lines of ————- are examples of lines of reflection.
symmetry
Reflections are isometric but do not preserve orientation.
true
reflection over the x-axis
(x, y) → (x, –y)
reflection over the y-axis
(x, y) → (–x, y)
reflection Over the line y = x:
(x, y) → (y, x)
reflection through the origin
(x, y) →(–x, –y)
Translations are a slide or shift.
Translations can be achieved by performing two composite reflections over parallel lines.
Translations are isometric, and preserve orientation.
true
(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.
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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.
true
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 360o or exhibit rotational
symmetry back onto itself.
Rotations of 180o are equivalent to a reflection through the origin.
Coordinate plane rules:
Counter-clockwise: Clockwise: Rule:
90o 270o
(x, y) (–y, x)
180o 180o
(x, y) (–x, –y)
270o 90o
(x, y) (y, –x)
true
