Compositions of Transformations. Review Name the Transformation Original Image Translation.

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Presentation transcript:

Compositions of Transformations

Review Name the Transformation Original Image Translation

Review Name the Transformation Original Image Rotation

Review Name the Transformation Original Image Reflection

Review Is this a Rigid Transformation Original Image No, it changes size

 Fill in the blank  The line of a reflection is the perpendicular bisector of every segment joining a point in the original figure with its image Review

 Name two types of symmetry  Reflectional  Rotational Review

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 Review

 Minimal path between points through a line  Reflect a point over the line and project a line straight to the reflected point Review

New Material Compositions of Transformations

 Composition – Applying more than one transformation to a figure

 Get your supplies  Patty Paper  Ruler

On a piece of patty paper, draw a small figure near one edge of the paper, and a line of reflection that does not intersect the figure Fold along the line of reflection, and trace the reflected image On your patty paper, draw a second reflection line parallel to the first so that the traced image is between the two parallel reflection lines

They are the same shape Translation How does the second traced image compare to the original figure? Name the single transformation that transforms the original to the second image

Use a ruler to measure the distance between a point in the original figure and its second image point. Compare this distance with the distance between the parallel lines. How do the distances compare? The images are twice as far apart as the parallel lines

 Reflection across Parallel Lines Conjecture A composition of two reflections across two parallel lines is equivalent to a singe translation. In addition, the distance from any point to its second image under the two reflections is twice the distance between the parallel lines.

 Get your supplies  Patty Paper  Protractor Each student needs one piece of patty paper

Same size and shape How does the second image compare to the original figure?

Rotation Name the single transformation form the original to the second image

How do the angles compare? The angle of rotation is twice the angle of the intersecting lines

 Reflections across Intersecting Lines Conjecture A composition of two reflections across a pair of intersecting lines is equivalent to a single rotation. The angle of rotation is twice the acute angle between the pair of intersecting reflection lines.

 page 386 #1-4, 11, 14-16