Coordinate Plane Rotations and Transformations

The video tutorial teaches how to graph an image after a rotation using coordinates. It begins with an introduction to rotating a triangle and reviewing the quadrants of the coordinate plane. The tutorial then explores 90° counterclockwise rotations, identifying patterns in coordinate changes, and forming a hypothesis. Further 90° rotations are tested to confirm the hypothesis. The video also covers 180° and 270° rotations, analyzing coordinate transformations and forming new hypotheses. The tutorial concludes with a summary of the learned concepts and encourages further exploration of clockwise rotations.

What remains unchanged during a rotation on the coordinate plane?

• Size, shape, and orientation

• Position and size

• Orientation and position

• Shape and position

In which quadrant are both x and y values positive?

• Quadrant 2

• Quadrant 1

• Quadrant 4

• Quadrant 3

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

• They become (y, -x)

• They become (-x, -y)

• They become (-y, x)

• They remain (x, y)

What is the new position of point B (4, 1) after a 90° counterclockwise rotation?

• (4, -1)

• (-4, -1)

• (1, -4)

• (-1, 4)

What is the hypothesis for a 90° counterclockwise rotation?

• Coordinates become (-y, x)

• Coordinates become (y, x)

• Coordinates become (x, -y)

• Coordinates remain the same

What happens to the coordinates (x, y) after a 180° counterclockwise rotation?

• They become (-x, -y)

• They become (y, x)

• They remain (x, y)

• They become (-y, x)

What is the hypothesis for a 180° counterclockwise rotation?

• Coordinates become (-x, -y)

• Coordinates become (x, y)

• Coordinates become (-y, x)

• Coordinates become (y, -x)

After a 270° counterclockwise rotation, what happens to the coordinates (x, y)?

• They become (-x, -y)

• They become (-y, x)

• They remain (x, y)

• They become (y, -x)

What is the hypothesis for a 270° counterclockwise rotation?

• Coordinates become (y, -x)

• Coordinates remain the same

• Coordinates become (-x, y)

• Coordinates become (-y, x)

In which quadrant are x values positive and y values negative?

• Quadrant 2

• Quadrant 3

• Quadrant 1

• Quadrant 4