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Triangle Transformations Exploration

Discover how applying multiple translations on a triangle's vertices results in compositions and equivalence with single translations. Learn how to return the triangle to its original position using specific transformations.

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Triangle Transformations Exploration

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  1. Section 7-3 Compositions of Transformations

  2. When you apply one transformation to a figure and then apply another transformation on its image, the result is called a composition.

  3. A triangle is drawn with vertices: (0,0), (4,0) and (2,5). Two translations are performed on the triangle. (x,y)  (x-6,y-4) and (x,y)  (x+14,y+3). What one single translation is equivalent to the composition of these two translations. What single translation will return the second image back to the original position?

  4. A triangle has vertices at (0,0), (4,0) and (2,5)

  5. Translate the triangle using the transformation (x,y)  (x-6,y-4) or

  6. Translate the new triangle using the transformation (x,y)  (x+14,y+3)

  7. Describe the one transformation that move the original triangle to the new position. (x,y)  (x-6,y-4) followed by (x,y)  (x+14,y+3) Becomes (x,y) (x+8, y-1)

  8. What one translation will return the second image back to the original? (x,y) (x-8, y+1)

  9. Reflections across 2 parallel lines

  10. Reflections across 2 Intersecting Lines

  11. Combining a translation with a reflection gives a special two-step transformation called a glide reflection.

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