The Algebra of Transformations

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The Algebra of Transformations

• Geo 14.3

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Homework Check 7 from handout

• Geo 14.3
• (reflecthw.gsp)

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Graph triangle A,B,C where A(0,2) B(2,2) and
C(2,1)

• Now consider the following transformation
  T(x,y) --gt (x-3, y2)
• Name A, B, C
• A B C
• Now Graph A,B, C. What transformation has
  occurred?

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Using your original points A(0,2) B(2,2) and
C(2,1)

• Now consider a different transformation T(x,y)
  --gt (2x, 2y)
• Name A, B, C
• A B C
• Now Graph A,B, C. What transformation has
  occurred?

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3 practice questions

• 1. Consider T(x,y) --gt (x 11, y - 4)
• A) Describe the transformation in words
• B) if (7,8) is on the pre-image, name a point
  on the image
• C) if (7,8) is on the image, name a point on the
  pre-image
• 2. what translation would map (-3,5) to (-10,
  11)? T(x,y) (_____, ______)

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Translation Explore (with Miras)

• Use a striaght edge to sketch and label any
  triangle ABC.
• Sketch two different parallel lines, m and n.

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Translation Explore (with Miras)

• Reflect ABC over m to create ABC
• Reflect ABC over n to create ABC

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What transformation occurred?

• Measure the distance AA in cm.
• Measure the (perpendicular) distance between m
  and n in cm.
• Make a conclusion in your groups