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 ID: 241931
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Slide1
Transformations and SymmetrySlide2
Vocabulary
Image
– The result of moving all points of a figure according to a transformationTransformation – The rule that assigns to each point of a figure another point in the planeSlide3
Vocabulary
Rigid Transformation, Isometry
– The image is congruent to the original figureNonrigid Transformation – A transformation that does not preserve the size and the shapeSlide4
Translation
Translation
– An isometry where each point is moved by the same translation vectorSlide5
TranslationSlide6
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 pointSlide7
Rotation
Rotation with Patty PaperSlide8
Reflection
Reflection
– An isometry in which each point and its image are on opposite sides and the same distance from a fixed lineSlide9
ReflectionSlide10
Investigation
Get your supplies
Straight Edge Patty PaperSlide11
Investigation
Draw a polygon and a line of reflection next to it on a piece of patty paperSlide12
Investigation
Fold your patty paper along the line of reflection and create the reflected image of your polygon by tracing itSlide13
Investigation
Draw segments connecting each vertex with its image point.
What conclusion can you draw comparing the segments and the line of reflectionSlide14
Investigation
Conjecture
The line of a reflection is the perpendicular bisector of every segment joining a point in the original figure with its imageSlide15
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 symmetrySlide16
Vocabulary
Rotational Symmetry
– The property that a figure coincides with itself under some rotationPoint Symmetry – The property that a figure coincides with itself under a rotation of 180°Slide17
Vocabulary
N-Fold Rotational Symmetry
– When the angle of rotation can be expressed as 360/n, for a positive value of nSlide18
Properties of IsometriesSlide19
Vocabulary
Ordered Pair Rules
– A rule that describes how to transform points on a coordinate planeSlide20
Transformation - ExampleSlide21
Investigation
Get your supplies
Graph paper Patty PaperSlide22
Investigation
Fold the graph paper both hot dog and hamburgerSlide23
Investigation
Fold the graph paper both hot dog and hamburgerSlide24
InvestigationSlide25
InvestigationSlide26
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 = xSlide27
Homework
7-1
page 372 #1-6, 12-167-2 page 381 #1-8, 13-17