Transformations and Symmetry

Vocabulary

Image – The result of moving all points of a figure according to a transformation

Transformation – The rule that assigns to each point of a figure another point in the plane

Vocabulary

Rigid Transformation, Isometry – The image is congruent to the original figure

Nonrigid Transformation – A transformation that does not preserve the size and the shape

Translation

Translation – An isometry where each point is moved by the same translation vector

Translation

Rotation

Rotation – An isometry in which each point is moved by the same angle measure in the same direction along a circular path about a fixed point

Rotation

Rotation with Patty Paper

Reflection

Reflection – An isometry in which each point and its image are on opposite sides and the same distance from a fixed line

Reflection

Investigation

Get your suppliesStraight EdgePatty Paper

Investigation

Draw a polygon and a line of reflection next to it on a piece of patty paper

Investigation

Fold your patty paper along the line of reflection and create the reflected image of your polygon by tracing it

InvestigationDraw segments connecting each

vertex with its image point.

What conclusion can you draw comparing the segments and the line of reflection

Investigation

ConjectureThe line of a reflection is the

perpendicular bisector of every segment joining a point in the original figure with its image

Vocabulary

Reflectional Symmetry – The property that a figure coincides with itself under a reflection (mirror symmetry)

Line of Symmetry – The line of reflection of a figure having reflectional symmetry

Vocabulary

Rotational Symmetry – The property that a figure coincides with itself under some rotation

Point Symmetry – The property that a figure coincides with itself under a rotation of 180°

Vocabulary

N-Fold Rotational Symmetry – When the angle of rotation can be expressed as 360/n, for a positive value of n

Properties of Isometries

Vocabulary

Ordered Pair Rules – A rule that describes how to transform points on a coordinate plane

Transformation - Example

Investigation

Get your suppliesGraph paperPatty Paper

Investigation

Fold the graph paper both hot dog and hamburger

Investigation

Fold the graph paper both hot dog and hamburger

Investigation

Investigation

Conjectures

The ordered pair rule (x,y) →(-x,y) is a reflection across the y-axis

The ordered pair rule (x,y) →(x,-y) is a reflection across the x-axis

The ordered pair rule (x,y) →(-x,-y) is a rotation about the origin

The ordered pair rule (x,y) →(y,x) is a reflection across the line y = x

Homework

7-1 page 372 #1-6, 12-16

7-2 page 381 #1-8, 13-17