Understanding Rotations in Geometry

The video tutorial covers the concept of rotation as a type of geometric transformation. It explains how rotations are performed around a fixed point, typically the origin, and how they result in congruent figures. The tutorial provides examples of matching diagrams with angles of rotation and solving for variables in isometric transformations. It also details the rules for 90-degree, 180-degree, and 270-degree rotations, emphasizing the changes in coordinates and signs. The video concludes with practical examples of applying these rotation rules to specific points.

What is the default direction assumed for a rotation if not specified?

• Clockwise

• Upward

• Downward

• Counterclockwise

In the first example, what is the angle of rotation for figure 1?

• 180 degrees

• 95 degrees

• 60 degrees

• 130 degrees

What is the result of a 360-degree rotation?

• The figure is enlarged

• The figure returns to its original position

• The figure is flipped

• The figure is rotated to a new position

If a rotation is isometric, what does it imply about the figures?

• They are similar

• They are congruent

• They are identical

• They are different

What is the rule for a 90-degree rotation in terms of coordinate mapping?

• (x, y) maps to (x, y)

• (x, y) maps to (-x, -y)

• (x, y) maps to (y, -x)

• (x, y) maps to (-y, x)

During a 180-degree rotation, what happens to the coordinates?

• They switch places

• They double in value

• They remain the same

• They change signs

What is the function rule for a 180-degree rotation?

• (x, y) maps to (y, -x)

• (x, y) maps to (-y, x)

• (x, y) maps to (-x, -y)

• (x, y) maps to (x, y)

What is the rule for a 270-degree rotation in terms of coordinate mapping?

• (x, y) maps to (y, -x)

• (x, y) maps to (-y, x)

• (x, y) maps to (-x, -y)

• (x, y) maps to (x, y)

In which quadrant does the image lie after a 270-degree rotation?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What happens to the x and y coordinates during a 270-degree rotation?

• They remain the same

• They both change signs

• They switch places and the new y changes sign

• They switch places and both change signs