Exploring Rotations in Geometric Transformations

The video tutorial covers the concept of rotation transformations, focusing on 90°, 180°, and 270° counterclockwise rotations. It explains the rules for each rotation type, demonstrating how to apply these rules to coordinates. The tutorial includes practical examples with a quadrilateral and offers a shortcut method for understanding rotations by physically rotating the paper. The video concludes with a summary and encouragement to practice the techniques.

What direction is typically used for geometric rotations unless stated otherwise?

• Horizontal

• Clockwise

• Counterclockwise

• Vertical

For a 90° counterclockwise rotation, how are the coordinates transformed?

• X becomes Y, Y becomes X

• X becomes -Y, Y becomes X

• Y becomes X, X becomes -Y

• Y becomes -X, X becomes Y

What happens to the coordinates in a 180° counterclockwise rotation?

• Both X and Y are negated

• No change to X and Y

• Both X and Y are doubled

• X and Y swap places

In a 270° counterclockwise rotation, how is the new Y coordinate determined?

• Original X negated

• Original Y negated

• Original Y

• Original X doubled

After plotting points A (3,7), B (7,6), C (7,4), and D (5,2), what is the next step in the demonstration?

• Verify the coordinates

• Rotate the points 90° counterclockwise

• Apply a 180° rotation

• Rotate the points 90° clockwise

What is the new location of point A after a 90° counterclockwise rotation from (3,7)?

• (-7,3)

• (-3,7)

• (7,-3)

• (3,-7)

How are the coordinates verified after rotating a quadrilateral 180° counterclockwise?

• By comparing to the original coordinates

• By using a protractor

• By measuring the angles

• By checking the side lengths

What practical shortcut is introduced for understanding rotations?

• Using a compass

• Drawing a new graph

• Using a calculator

• Rotating the paper physically

After rotating the paper 90° counterclockwise, where does point A (5,1) move to?

• (1,5)

• (-1,-5)

• (1,-5)

• (-5,1)

What is the result for point B after a total of 270° rotation counterclockwise?

• (-1,2)

• (2,-1)

• (-2,1)

• (1,-2)