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Aim: What do we remember Aim: What do we remember about transformations?about transformations?Do Now:Do Now: Circle what changes in each of the
following:
Translation: Location Size Orientation
Dilation: Location Size Orientation
Reflection: Location Size Orientation
Rotation: Location Size Orientation
Review TranslationsReview Translations
Regents Question: Pair/Share: Which of the following translations best describes the diagram below?
a. 3 units right and 2 units down
b. 3 units left and 2 units up
c. 3 units left and 2 units up
Review DilationsReview DilationsSome things to remember: When dilating by a scale
factor less than one, the figure becomes smaller.
Opposite this, when dilating by a scale factor greater than one the figure becomes larger.
To calculate a dilation, multiply the x and y values of each point by the scale factor.
Regents Question: Graph triangle ABC and its image under D3.
A(2,3), B(2,-1), C(-1,-1)
Review ReflectionsReview Reflections
Pair/Share: Do you remember the three types of reflections?
line reflection
point reflection
glide reflection
Line ReflectionsLine Reflections
Some things to remember:
ry=x (x,y) becomes (y,x)
ry=-x (x,y) becomes (-y,-x)
rx-axis (x,y) becomes (x,-y)
ry-axis (x,y) becomes (-x,y)
Regents Question: Angle ABC has been reflected in the x-axis to create angle A'B'C'. Prove that angle measure is preserved under a reflection.
It appears that the angles may be right angles. Let's see if this is true using slopes.
Since these slopes are negative reciprocals, these segments are perpendicular, meaning m<ABC =
90º.
Since these slopes are negative reciprocals, these segments are perpendicular, meaning m<A'B'C' =
90º. Angle measure is preserved.
Point ReflectionsPoint Reflections
Some things to remember:
R(0,0)
(x,y) becomes (-x,-y)
Regents Question: Pair/Share: When dealing with a point reflection in the origin, the origin is the midpoint of the line segments connecting each point to its image.
True False
Glide ReflectionsGlide Reflections
Some things to remember:
a combination of a line reflection and a translation parallel to the line
Regents Question: Given triangle ABC: A(1,4), B(3,7), C(5,1); Graph and label the following composition:
Triangle A'B'C' is the reflection in the x-axis. Then triangle A''B''C'' is the translation of T(-5,-2). A''(-4,-6),
B''(-2,-9), C''(0,-3)
RotationsRotationsSome things to remember:
R90 (x,y) becomes (-y,x)
R180 (x,y) becomes (-x,-y)
R270 (x,y) becomes (y,-x)
positive rotations are counter-clockwise
Regents Question: A(2,3), B(2,-1), C(-1,-1) Graph triangle ABC under the following rotations:
RED
GREEN
MAGENTA
SymmetriesSymmetries
Some things to remember: Line symmetry occurs when two halves of a figure
mirror each other across a line Point symmetry occurs when the center point is a
midpoint to every segment formed by joining a point to its image
Rotational symmetry occurs if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same
Regents questions: Pair/Share:
If the alphabet were printed in simple block printing, which capital letters would have BOTH vertical and
horizontal symmetry?
Does the word NOON possess point symmetry?
IsometriesIsometries
An isometry is a transformation of the plane that preserves length.
A direct isometry preserves orientation or order.
A non-direct or opposite isometry changes the order (such as clockwise changes to counterclockwise).