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Composition of Transformations

Composition of Transformations. Section 9.5. Composition of Transformations. When two or more transformations are combined to form a single transformation, the result is a composition of transformations. Composition of Transformations.

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Composition of Transformations

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  1. Composition of Transformations Section 9.5

  2. Composition of Transformations • When two or more transformations are combined to form a single transformation, the result is a composition of transformations.

  3. Composition of Transformations • The endpoints of RS are R(1, -3) and S(2, -6). Graph the image of RS after the composition. • Reflection in the y-axis • Rotation 90o about the origin

  4. Glide Reflection • A glide reflection is an example of a composition of transformations in which every point P is mapped to a point P’’ by the following steps. • A translation maps P to P’ • A reflection in a line k parallel to the direction of the translation maps P’ to P’’

  5. Glide Reflection • The vertices of Triangle ABC are A(3, 2), B(6, 3) and C(7, 1). Find the image of Triangle ABC after the glide reflection • (x, y)→(x – 12, y) • Reflection in the x-axis

  6. Reflection in Parallel Lines Theorem • If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is the same as a translation.

  7. Reflection in Intersecting Lines Theorem • If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is the same as a rotation about point P. • The angle of rotation is 2xo, where xo is the measure of the acute or right angle formed by k and m.

  8. Assignment • p.611: 3-10

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