Rotations Investigation

Rotations

Below you see a computer-generated rotation. When you move the green slider, it will make the transformed shape rotate by the given degrees. The table to the right of it shows the coordinates of the original shape (Point A, Point B, and Point C) and the transformed shape (Point A', Point B', and Point C').[br][br]Play around with the slider and see if you can find any patterns with the points as you rotate. You can also drag Point A, Point B, and Point C around and see how that affects the coordinates in the table[br][br]When you are done investigating, answer the questions below. For each, there is only one answer, and you leave the wrong answers blank. You should check your answers after each!

Investigating Rotations

Move the slider (the green circle). It will make a transformed shape rotate. When you move the slider to the left (the negative direction), which direction is that?

Counterclockwise Clockwise

90 degrees counterclockwise

When you rotate 90 degrees counterclockwise, what happens with the points?

(x, y) --> (y, -x) (x, y) --> (-y, -x) (x, y) --> (-y, x) (x, y) --> (y, x)

90 degrees clockwise

When you rotate 90 degrees clockwise, what happens with the points?

(x, y) --> (y, x) (x, y) --> (-y, -x) (x, y) --> (-y, x) (x, y) --> (y, -x)

Reflections

Below you see two computer-generated reflections: one about the y-axis and one about the x-axis. [br][br]Drag Point A, Point B, and Point C around and see how that affects the coordinates in the table. Can you see a pattern in the points?[br][br]When you are done investigating, answer the questions below. There could be more than one answer. You check your answers after each.

Investigating Reflections about the y-axis

Investigating Reflections about the x-axis

When you reflect about the y-axis, what happens with the points?

(x, y) --> (x, -y) (x, y) --> (y, x) (x, y) --> (-x, y) (x, y) --> (-y, -x)

When you reflect about the x-axis, what happens with the points?

(x, y) --> (-y, -x) (x, y) --> (-x, y) (x, y) --> (y, x) (x, y) --> (x, -y)

Comparing Rotations and Reflections

Below are some general questions. See if you can get them right! There can be more than one answer for each question, or even NO answers

Which transformation switches the x- and y-coordinates?

90 degree clockwise rotation about the origin 180 degree rotation about the origin 270 degree clockwise rotation about the origin 90 degree counterclockwise rotation about the origin Reflection about the y-axis Reflection about the x-axis 270 degree counterclockwise rotation about the origin

Which transformation keeps the x- and y-coordinates in the same place?

270 degree counterclockwise rotation about the origin Reflection about the x-axis 180 degree rotation about the origin 270 degree clockwise rotation about the origin 90 degree counterclockwise rotation about the origin Reflection about the y-axis 90 degree clockwise rotation about the origin

Which transformations change the sign of only the x-coordinate?

Reflection about the x-axis Reflection about the y-axis 270 degree clockwise rotation about the origin 90 degree clockwise rotation about the origin 90 degree counterclockwise rotation about the origin 270 degree counterclockwise rotation about the origin 180 degree rotation about the origin

Which transformations change the sign of only the y-coordinate?

90 degree counterclockwise rotation about the origin Reflection about the y-axis 270 degree counterclockwise rotation about the origin 270 degree clockwise rotation about the origin 90 degree clockwise rotation about the origin 180 degree rotation about the origin Reflection about the x-axis

Which transformations keep the signs of both coordinates?

180 degree rotation about the origin 90 degree clockwise rotation about the origin 90 degree counterclockwise rotation about the origin Reflection about the y-axis 270 degree counterclockwise rotation about the origin 270 degree clockwise rotation about the origin Reflection about the x-axis

Which transformations change the signs of both coordinates?

Reflection about the y-axis 270 degree clockwise rotation about the origin Reflection about the x-axis 90 degree clockwise rotation about the origin 270 degree counterclockwise rotation about the origin 90 degree counterclockwise rotation about the origin 180 degree rotation about the origin