Level 372 Level 374
Level 373

Translations, Reflections & Rotations


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*Translations*
When you slide one figure from one position to another.
A slide!
What is another word for translations?
*Reflections*
When you flip a figure over a line.
A flip!
What is another word for reflection?
Reflect over x-axis means...
x-coordinates stay the same, y-coordinates are opposites.
Reflect over the y-axis means...
y-coordinates stay the same, x-coordinates are opposites.
*Rotations*
90 degree clockwise, 180 degree clockwise, & 270 degree clockwise.
y-Coordinate
The vertical measure, which is the second number in an ordered pair.
x-Coordinate
is the first number in an ordered pair and it represents the location relative to the x-axis.
add!
Up and Right:
subtract!
down and Left:
(x,y)-(x,-y)
reflecting over x-axis
(x,y)-(-x,y)
reflecting over y-axis
y=x
(x,y)-(y,x)
(x,y)-(y,-x)
Rotating 90 cw
(x,y)-(-y,x)
Rotating 90 ccw
(x,y)-(-x,-y)
rotating 180
image
the resulting figure AFTER a transformation is performed on it
Preimage
The image that I start with is called:
translation
It is a transformation that moves points the distance and in the same direction.
Isometry
a transformation that does not change the size or shape of a figure
Translation Theorem
A translation is an isometry.
reflection
It is a transformation that flips a figure over a line of reflection.
mirror line
Line of Reflection
(a, -b)
Reflection in the x-axis
(-a, b)
Reflection in the y-axis
(b, a)
Reflection when y= x
(-b, -a)
Reflection when y= -x
Reflection Theorem
A reflection is an isometry.
rotation
It is a transformation that turns a figure about a fixed point.
Center of Rotation
point around which a figure rotates
angle of rotation
formed by rays drawn from the center of rotation to a point and its image
90 Rotation
(-b, a)
180 Rotation
(-a, -b)
270 Rotation
(b, -a)
Rotation Theorem
A rotation is an isometry.