Rotating Images Around the Origin in Geometry

The video tutorial introduces the concept of rotations in geometry, explaining how shapes are rotated around a center point without changing size. It covers the directions of rotation, specifically counterclockwise, and introduces notations like R90, R180, and R270. The tutorial provides rules for transforming points during rotations and demonstrates a practical example of a 90-degree rotation around the origin, highlighting the transformation of coordinates.

What is the center of rotation?

• The point that changes size during rotation

• The point where the shape ends its rotation

• The point that remains fixed while the shape rotates

• The point where the shape starts rotating

In which direction do we assume rotations occur for this lesson?

• Clockwise

• Upwards

• Counterclockwise

• Downwards

What is the notation for a 90-degree rotation?

• R 360

• R 90

• R 180

• R 270

How many degrees is a half turn around a circle?

• 270 degrees

• 180 degrees

• 360 degrees

• 90 degrees

What happens to the coordinates of a point during a 90-degree counterclockwise rotation?

• The coordinates remain the same

• The x and y coordinates switch places and the new x coordinate changes sign

• The x and y coordinates switch places and the new y coordinate changes sign

• Both coordinates change sign

What is the rule for a 180-degree rotation?

• Change the sign of the x coordinate

• Change the sign of both coordinates

• Change the sign of the y coordinate

• Switch the x and y coordinates

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

• They are unrelated

• They are opposite

• One is double the other

• They are the same

What is the new coordinate of point A (-4, -1) after a 90-degree counterclockwise rotation?

• (1, -4)

• (-4, 1)

• (4, 1)

• (-1, 4)

What is the new coordinate of point B (-3, 5) after a 90-degree counterclockwise rotation?

• (5, -3)

• (-5, 3)

• (3, -5)

• (-3, 5)

What is the new coordinate of point C (-1, 3) after a 90-degree counterclockwise rotation?

• (3, -1)

• (-3, 1)

• (1, -3)

• (-1, 3)