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90 Degree Rotation about ANY POINT: Quick Exploration

Author:Tim Brzezinski

Here, the LARGE POINTS are moveable. Go move points around, play around, and explore! Don't forget the slider. :)

Move the slider all the way to the left (so only 1 right triangle shows). Be sure the center of rotation = (0,0). Move the WHITE POINT and PREIMAGE point anywhere you want. Then answer the following questions. Be sure to number your responses in your answer:

  1. What are the coordinates of the PREIMAGE?
  2. What is the slope of the hypotenuse of the original right triangle?
  3. What is the slope of the hypotenuse of the rotated right triangle?
  4. What are the coordinates of the IMAGE?

Use this app to answer the next few questions.

Move the center of rotation to (2,1). Move the PREIMAGE point to (3,5). Then slide the slider slowly to the right. In the space below, please answer the following:

  1. What is the slope of the hypotenuse of the original right triangle?
  2. What is the slope of the hypotenuse of the rotated right triangle?
  3. What are the coordinates of the IMAGE?

Is there any relationship between the slope of the original right triangle and the slope of the right triangle that's been rotated 90 degrees? If so, how would you describe it?

How can we use the following data

  • slope of hypotenuse of original right triangle
  • slope of hypotenuse of right triangle rotated 90 degrees
  • coordinates of the PREIMAGE
to determine the coordinates of the IMAGE of any point rotated 90 degrees about any other point (other than (0,0)) in the coordinate plane? Explain.

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