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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.
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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
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
Investigation • Get your supplies Straight Edge Patty 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
Investigation • Draw segments connecting each vertex with its image point. • What conclusion can you draw comparing the segments and the line of reflection
Investigation • Conjecture • The 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
Vocabulary • Ordered Pair Rules – A rule that describes how to transform points on a coordinate plane
Investigation • Get your supplies Graph paper Patty Paper
Investigation Fold the graph paper both hot dog and hamburger
Investigation Fold the graph paper both hot dog and hamburger
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