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GeoGebra

Composition of Transformations Activity

Author:Bo Gilbert, Jed Butler
Use the checkboxes to choose 1 or 2 transformations. The decorate box can be chosen to show congruent corresponding sides. Take a moment to explore what you can do.

Questions to consider as we work through this activity.

1) Is there more than one combination of transformations that gives the same final product? 2) Does the order in which we transform the object matter?
Task 1 Use the applet below to complete the following tasks.

Part 1

Translate the triangle 7 units left and 3 units down. *Note: You are moving the orange point with the word drag above it.] What is the coordinate notation for this transformation?

Select all that apply
  • A
  • B
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  • D
Check my answer (3)

Part 2

Next, reflect the new triangle over the x-axis. *Note: Make sure you click on the button that says "I need another transformation" first. What is the coordinate notation for this transformation?

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  • A
  • B
  • C
  • D
Check my answer (3)

Part 3

What is the coordinate notation that will take you from the original triangle to the third triangle? [Hint: Think about the order in which we did the transformations.]

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Check my answer (3)
Task 2 Use the applet below to help answer the following questions.

Question 1

Place point A at the coordinates (3, 5). What will be the image of A be after a rotation of 90 degrees counter-clockwise followed by a translation 5 units up? Be sure to type your answer as an ordered pair.

Check my answer

Question 2

Raphael and Michelangelo were both asked to use coordinate notation to describe the result of a translation 4 units left and 1 unit up, followed by a reflection across the y-axis. Raphael wrote the following notation: (x,y) -> (-x + 4, y + 1). Donatello wrote the following notation: (x,y) -> (-[x - 4], y + 1). Who is correct?

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Question 3

Use the applet below to answer this question. Describe the combination of transformations that could have occurred going from the gray triangle to the the pink triangle.

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  • A
  • B
  • C
  • D
Check my answer (3)

Question 4

Is there another way to get the same transformation to happen as in question 3? If so, explain your sequence of transformations. Use the applet below to explore.

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