Rotations and Coordinate Transformations

The video tutorial explains how to graph images after rotations using coordinates. It begins with a review of the coordinate plane quadrants and explores the effects of 90-degree counterclockwise rotations, identifying patterns in coordinate changes. The tutorial then extends these observations to rotations across different quadrants, forming hypotheses for 180 and 270-degree rotations. The video emphasizes understanding coordinate transformations without relying on graphs and encourages verifying hypotheses through experimentation.

What remains unchanged during a rotation on the coordinate plane?

• Orientation and position

• Shape and position

• Position and size

• Size, shape, and orientation

In which quadrant are both x and y values positive?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

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

• (y, -x)

• (-y, x)

• (-x, -y)

• (x, y)

What is the new position of point A (2, 1) after a 90-degree counterclockwise rotation?

• (2, -1)

• (-2, 1)

• (-1, 2)

• (1, -2)

What is the pattern observed in a 90-degree counterclockwise rotation from quadrant 2 to quadrant 3?

• Only x changes sign

• x and y remain the same

• x and y switch, x changes sign

• x and y switch, y changes sign

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

• (x, y) becomes (y, -x)

• (x, y) becomes (-y, x)

• (x, y) becomes (-x, -y)

• (x, y) becomes (x, y)

During a 270-degree counterclockwise rotation, what happens to the coordinates (x, y)?

• (-y, -x)

• (y, -x)

• (-x, y)

• (y, x)

What is the new position of point B (3, 1) after a 270-degree counterclockwise rotation?

• (-3, 1)

• (3, -1)

• (1, -3)

• (-1, 3)

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

• x and y switch, y becomes negative

• Only y changes sign

• x and y switch, x becomes negative

• x and y remain the same

What should you do to verify the hypotheses about rotations?

• Ignore the patterns

• Conduct more experiments

• Rely on the given examples

• Use a different coordinate system