Graphing Rotations Using Coordinates

The video tutorial explains how to graph images after rotations using coordinates. It covers 90, 180, and 270-degree counterclockwise rotations, emphasizing the changes in x and y coordinates. The tutorial introduces hypotheses for each rotation type and encourages verification through pattern recognition. It also reviews the quadrants of the coordinate plane and highlights the importance of understanding coordinate transformations.

What remains unchanged during a rotation on the coordinate plane?

• Quadrants

• Coordinates

• Size, shape, and orientation

• Position

In a 90-degree counterclockwise rotation, how do the coordinates (x, y) transform?

• (y, -x)

• (-x, -y)

• (x, y)

• (-y, x)

Which quadrant does a figure move to after a 90-degree counterclockwise rotation from Quadrant I?

• Quadrant I

• Quadrant II

• Quadrant IV

• Quadrant III

What is the pattern observed in the coordinates after a 90-degree counterclockwise rotation from Quadrant II to Quadrant III?

• Both x and y become positive

• x and y switch places, and x changes sign

• x and y switch places, and y changes sign

• Coordinates remain the same

What is the hypothesis for the transformation of coordinates after 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, how do the coordinates (x, y) change?

• (x, y) becomes (x, y)

• (x, y) becomes (-y, x)

• (x, y) becomes (-x, -y)

• (x, y) becomes (y, -x)

Which quadrant does a figure move to after a 270-degree counterclockwise rotation from Quadrant III?

• Quadrant I

• Quadrant II

• Quadrant IV

• Quadrant III