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GeoGebra

Exploring Transformations - Rotations

Author:Megan Dougherty, Jon Ingram
Topic:Rotation

Exploring Rotations

Take a few minutes to explore rotating the figure below. You can choose what is shown on your graph using the checklist in the upper left hand corner of the screen, and you can move the vertices of the source triangle and center or rotation to manipulate the image.

Task 1

Once you have had a chance to explore, reset your image so it in the following location: The point of rotation is the origin (0,0) The vertices of the triangle are at the following points - (2,2) (3,2) and (2,4)

Q1

Rotate the triangle counter clockwise about the origin. Record the new points below, then tell what happened to each x and y value.

Q2

Rotate the triangle  counter clockwise about the origin. Record the new points below, then tell what happened to each x and y value.

Q3

Rotate the triangle counter clockwise about the origin. Record the new points below, then tell what happened to each x and y value.

Q4

What general rule could you come up with to represent the points of figured that are rotated 90, 180 and 270 degrees counter clockwise about the origin?

Task 2

Keep your triangle in the same location at (2,2) (3,2) and (2,4) but move your point of rotation away from the origin (you choose where)

Q1

Do our general rules for points being rotated 90, 180 and 270 degrees counter clockwise about the origin remain true? Why or why not?

Q2

Keep your image rotated counter clockwise, then move the center of rotation around. What happens to the image?

Q3

Specifically, what can we generalize about the relationship between the different points of the triangle and the center of rotation? HINT: If you need help with this, look at the purple points and their relationship with the center when the center is at (1,2) then (0,2) then (-1,2) and ect.

Q4

How might you be able to determine the center of rotation if it was hidden?

Task 3

Create a new polygon (try something other than a triangle!) and rotate it about a point. Use line segments and measure tool to prove your theory about the relationship between the points of a figure and the center of rotation.

Q1

Use the angle measure tool to measure the angle your two line segments make. How does this relate to your degree of rotation?

Q2

Pretend you are drawing a rotation on a piece of paper. What are the steps you would take to draw a rotation of a figure 45 degrees counter clockwise about a point of rotation?

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