9.5 & 9.6 – Compositions of Transformations & Symmetry

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Transcript of 9.5 & 9.6 – Compositions of Transformations & Symmetry

  • 9.5 & 9.6 Compositions of Transformations & Symmetry

  • Glide Reflection:A transformation with a translation and then a reflection in a line parallel to the direction of the translationPQk

  • Composition of Transformations:Any two transformations combined to form a single transformation

  • If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is a ___________. If ____ is the image of P after the two reflections, then:translation

  • If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is a _________. If ____ is the image of P after the two reflections, then:rotation The angle of rotation is 2x, where x is the measure of the acute or right angle formed by k and m

  • Graph the image of A(1, 2) after the described glide reflection.1. Translation: (x, y) (x + 2, y) Reflection: in the x-axisA

  • Graph the image of A(1, 2) after the described glide reflection.2. Translation: (x, y) (x 1, y + 3) Reflection: in x = 2 A

  • The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3). Graph the image of ABC after a composition of the transformations in the order they are listed.ABCReflection: y-axisTranslation: (x, y) (x + 3, y 5)

  • The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3). Graph the image of ABC after a composition of the transformations in the order they are listed.Reflection: y = 1Reflection: y = xABC(y, x)(x, y) (3, 1)(1, 3)(1, 3)(3, 1)(5, 1)(1, 5)

  • Describe the composition of transformations.Reflection:x-axisTranslation:(x, y) (x + 6, y + 2)

  • Describe the composition of transformations.Rotation:90Reflection:x-axis

  • In the diagram, is reflected in line r, and is reflected in line s.7. A translation maps onto which segment?

  • In the diagram, is reflected in line r, and is reflected in line s.8. Which lines are perpendicular to r and s

  • In the diagram, is reflected in line r, and is reflected in line s.9. Name a segment parallel to

  • In the diagram, is reflected in line r, and is reflected in line s.10. If the distance between r and s is 2.4 inches, what is the length of 2.4 24.8 inches

  • In the diagram, is reflected in line r, and is reflected in line s.11. Is the distance from to r the same as the distance from C to r? Yes,Def. of Reflection

  • 12. Find the angle of rotation that maps T onto 75 2150

  • 13. Find the angle of rotation that maps A onto 99 2198

  • Line of Symmetry:The figure can be mapped onto itself by a reflection in the lineRotational Symmetry:The figure can be mapped onto itself by a rotation of 180 or less around a point

  • Identify the number of line and rotational symmetry of the figure shown.Line: _____________Rotational: _________1none

  • Identify the number of line and rotational symmetry of the figure shown.Line: _____________Rotational: _________nonenone

  • Identify the number of line and rotational symmetry of the figure shown.3120360 3=120Line: _____________Rotational: _________

  • 90, 180360 4=90Identify the number of line and rotational symmetry of the figure shown.Line: _____________Rotational: _________4

  • 60, 120, 360 6=60Identify the number of line and rotational symmetry of the figure shown.Line: _____________Rotational: ____________6180

  • Identify the number of line and rotational symmetry of the figure shown.Line: _____________Rotational: _________1none

  • Identify the number of line and rotational symmetry of the figure shown.490, 180360 4=90Line: _____________Rotational: _________

  • Identify the number of line and rotational symmetry of the figure shown.1noneLine: _____________Rotational: _________

  • Identify the number of line and rotational symmetry of the figure shown.2Line: _____________Rotational: _________180 360 2=180

  • HW Problems9.5 #13Translation:Rotation:180(x, y) (x + 5, y + 1)

    9.59.6611-612621-6233, 6, 9, 11, 13-21 all3, 4, 6, 7, 9, 11, 12