Mastering Adding and Subtracting Rational Expressions

The video tutorial covers the concept of rotations about the origin, explaining how figures rotate around a fixed point, typically the origin, at specific angles and directions. It introduces the grid and quadrants, and how to derive and apply rotation rules for 90, 180, and 270 degrees. The tutorial emphasizes understanding over memorization, showing how to quickly derive rules for both counterclockwise and clockwise rotations.

What is the most common center of rotation?

• A fixed point on the figure

• The origin

• The midpoint of the figure

• A random point on the grid

In which direction does a standard 90-degree rotation move?

• Clockwise

• Counterclockwise

• Upwards

• Downwards

What happens to the coordinates (x, y) in a 90-degree counterclockwise rotation?

• They switch places and the y-value changes sign

• They switch places and the x-value changes sign

• They remain the same

• Only the x-value changes sign

How do the coordinates (x, y) change in a 180-degree rotation?

• They switch places and both change signs

• They remain the same

• They change signs but do not switch places

• Only the y-value changes sign

What is the new coordinate of (2, 1) after a 270-degree counterclockwise rotation?

• (1, -2)

• (-1, 2)

• (-2, -1)

• (2, -1)

How can you quickly find the rule for a 90-degree counterclockwise rotation?

• Memorize the rule

• Switch the coordinates and change the sign of the y-value

• Switch the coordinates and change the sign of the x-value

• Only change the sign of the x-value

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

• Only change the sign of the x-value

• Only change the sign of the y-value

• Switch the coordinates and change the sign of the x-value

• Switch the coordinates and change the sign of the y-value

How do you derive the rule for a 270-degree clockwise rotation?

• Use the rule for a 90-degree counterclockwise rotation

• Use the rule for a 360-degree counterclockwise rotation

• Use the rule for a 180-degree counterclockwise rotation

• Use the rule for a 270-degree counterclockwise rotation

What is the new coordinate of (3, 4) after a 270-degree clockwise rotation?

• (-3, -4)

• (3, -4)

• (-4, 3)

• (4, -3)

What is the relationship between 90-degree clockwise and 270-degree counterclockwise rotations?

• They are opposite

• They are both 180-degree rotations

• They are the same

• They are unrelated