Rotation Rules and Transformations

The video tutorial covers isometry transformations focusing on rotations. It explains how to perform 90-degree, 180-degree, and 270-degree counterclockwise rotations around the origin, detailing the changes in coordinates. The tutorial also discusses the equivalence of certain counterclockwise and clockwise rotations, providing rules for each. The video concludes with a summary of the rotation concepts and their applications.

What is the main focus of the video on isometry transformations?

• Scaling

• Reflection

• Rotation

• Translation

When rotating a triangle counterclockwise around the origin, what is the center of rotation?

• Point (3,3)

• Point (2,2)

• Point (1,1)

• Point (0,0)

What is the rule for a 90-degree counterclockwise rotation?

• Switch x and y, multiply new y by -1

• Switch x and y, multiply new x by -1

• Switch x and y, multiply both by -1

• Multiply both x and y by -1

After applying the 90-degree rotation rule, what is the new position of point (4,7)?

• (-4,7)

• (4,-7)

• (7,-4)

• (-7,4)

How can you verify that a rotation has occurred using a compass?

• By measuring the angle between the original and new point

• By measuring the distance from the center to the point

• By checking the color of the point

• By counting the number of rotations

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

• Switch x and y, multiply new y by -1

• Switch x and y, multiply both by -1

• Switch x and y, multiply new x by -1

• Multiply both x and y by -1

What is the new position of point (4,7) after a 180-degree rotation?

• (-7,4)

• (7,-4)

• (4,-7)

• (-4,-7)

What is the rule for a 270-degree counterclockwise rotation?

• Switch x and y, multiply new y by -1

• Switch x and y, multiply both by -1

• Switch x and y, multiply new x by -1

• Multiply both x and y by -1

What is the new position of point (4,7) after a 270-degree rotation?

• (7,-4)

• (-7,4)

• (-4,7)

• (4,-7)

How does a 270-degree counterclockwise rotation compare to a 90-degree clockwise rotation?

• One is faster than the other

• They result in the same position

• They are opposite

• They are different