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).