Exploring the Rotation of Geometric Figures

The video tutorial covers the concept of rotation as a geometric transformation. It explains how rotation can occur at any angle around a central point, either clockwise or counterclockwise. The tutorial focuses on rotations of 90 degrees clockwise, 90 degrees counterclockwise, and 180 degrees around the origin. It provides rules for each type of rotation, demonstrating how coordinates change during these transformations. Practical examples are given to illustrate these concepts, showing how points on a plane are affected by different rotations.

What are the two directions in which rotation can occur?

• Clockwise and counterclockwise

• Forward and backward

• Upward and downward

• Left and right

What happens to the coordinates (x, y) when rotated 90 degrees clockwise?

• They become (-x, -y)

• They become (-y, x)

• They become (y, -x)

• They remain the same

If a point at (0, 4) is rotated 90 degrees clockwise, where does it move?

• (4, 0)

• (0, -4)

• (-4, 0)

• (0, 4)

What is the general rule for rotating a point 90 degrees counterclockwise?

• (x, y) becomes (-x, -y)

• (x, y) becomes (x, y)

• (x, y) becomes (-y, x)

• (x, y) becomes (y, -x)

When rotating 90 degrees counterclockwise, what happens to the x-values?

• They become the new y-values without changing sign

• They remain the same

• They become the new y-values and change sign

• They become the new x-values without changing sign

What is the general rule for rotating a point 180 degrees?

• (x, y) becomes (-x, -y)

• (x, y) becomes (-y, x)

• (x, y) becomes (x, y)

• (x, y) becomes (y, -x)

If a point at (-3, -1) is rotated 180 degrees, where does it move?

• (-3, -1)

• (-3, 1)

• (3, 1)

• (3, -1)

What happens to the coordinates (x, y) when rotated 180 degrees?

• They remain the same

• They become (-x, -y)

• They become (y, -x)

• They become (-y, x)

If a point at (-1, 3) is rotated 90 degrees clockwise, where does it move?

• (3, 1)

• (-1, 3)

• (-3, -1)

• (1, -3)

When rotating 90 degrees clockwise, what happens to the y-values?

• They remain the same

• They become the new x-values and change sign

• They become the new y-values and change sign

• They become the new x-values without changing sign