Exploring Rotations on the Coordinate Plane

This video tutorial covers the concept of rotations on the coordinate plane, explaining what a rotation is and how it can be represented algebraically. It discusses the center of rotation, typically the origin, and describes rotations in terms of direction (clockwise or counterclockwise) and degrees (90, 180, 270, 360). The tutorial provides examples of rotations, showing how to calculate the degree of rotation by counting quadrants. It also explains how to represent rotations algebraically by examining changes in ordered pairs and provides practice problems to reinforce these concepts.

What is the center of rotation typically used in the examples?

• The origin (0,0)

• Point (1,1)

• Point (2,2)

• None of the above

What direction does a clockwise rotation move?

• Downwards

• To the right

• To the left

• Upwards

How many degrees does moving one quadrant represent?

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

What is the result of a 180-degree rotation?

• Point moves two quadrants

• Point does not move

• Point moves three quadrants

• Point returns to original position

What happens to the coordinates in a 90-degree clockwise rotation?

• x becomes y, y becomes -x

• x becomes -y, y becomes x

• x and y swap places without sign change

• No change to coordinates

Which of the following represents a 270-degree clockwise rotation?

• x becomes y, y becomes -x

• y becomes -x, x becomes y

• y becomes x, x becomes -y

• x becomes -y, y becomes x

How is a 180-degree rotation algebraically represented?

• (x, y) becomes (-x, -y)

• (x, y) becomes (y, x)

• (x, y) becomes (x, y)

• (x, y) becomes (-y, -x)

If a point is rotated 270 degrees clockwise, how many quadrants does it move?

• Two quadrants

• One quadrant

• Four quadrants

• Three quadrants

Using the rule (x, y) becomes (-y, x), what is the new coordinate of (3, 4)?

• (-3, 4)

• (3, -4)

• (4, -3)

• (-4, 3)

What is the algebraic rule for a rotation that results in the coordinates (8, 9) from (-8, -9)?

• (x, y) becomes (-y, -x)

• (x, y) becomes (y, x)

• (x, y) becomes (-x, -y)

• (x, y) becomes (x, y)