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WARM UP TUESDAY FEBRUARY 4, 2014

WARM UP TUESDAY FEBRUARY 4, 2014. Rotate P(-4, -4) 180  2. Rotate Q(-1, -3) 90  CCW . EOCT. Glide Reflections and Compositions . Compositions. Two or more transformations are combined to produce a single transformation ( ie Rotation & Reflection)

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WARM UP TUESDAY FEBRUARY 4, 2014

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  1. WARM UP TUESDAY FEBRUARY 4, 2014 • Rotate P(-4, -4) 180 2. Rotate Q(-1, -3) 90 CCW

  2. EOCT

  3. Glide Reflections and Compositions

  4. Compositions • Two or more transformations are combined to produce a single transformation (ie Rotation & Reflection) • The composition of 2 (or more) isometries is an isometry.

  5. Finding the Image of a Composition C’(2, 0), D’(3, –3) Perform the following composition on C(2, 0), D(3, 3) C’’(0, –2), D’’(–3, –3)

  6. YOU TRY! Perform the composition on ∆ABC A(2,1) B(3,3) C(1,4) Rotate 180º about the origin A’(-2,-1) B’(-3,-3) C’(-1,-4) Reflect over the y-axis A’’(2,-1) B’’(3,-3) C”(1,-4)

  7. Glide Reflections Combining, a translation with a reflection If the line of reflection is parallel to the direction of translation, then it does not matter which you do first. Otherwise, order is important.

  8. 1. Finding the Image of a Glide Reflection Use the information below to sketch the image of QRS after a glide reflection. Q(2, –3), R(4, –4), and S(5, –1) Q’’(-2, 2), R’’(-4, 1), S’’(-5, 4)

  9. YOU TRY! Perform the Glide Reflection on ∆ABC A(4,-1) B(4,-3) C(-1,4) Translate: (x, y)→ (x +2, y-1) A’(6,0) B’(6,-4) C’(1, 3) Reflect over y=x A’’(0,6) B’’(-4,6) C”(3,1)

  10. Dilations NOT an isometry. Dilations are a resizing of the image. They change the lengths of the segments but NOT the ANGLES. If the scale factor is greater than 1 the figure becomes larger. X > 1 If the scale factor is less than 1 but greater than 0 the figure becomes smaller. 0 < X < 1

  11. Example Use the given scale factor to find the vertices of the image for the polygon. k= 1/3 A(3, 9) → B(12,-3) → C(-1, -6) → D(15, 900) → A’(1, 3) B’(4, -1) C’(-1/3, -2) D’(5, 300)

  12. YOU TRY! Use the given scale factor to find the vertices of the image for the triangle. k = 10 A(.5, 2) B(1,-3) C(-.1, -9)

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