Rotating Shapes Around Non-Origin Points

The video tutorial explains how to rotate images around a center that is not the origin. Initially, it reviews the simple rotation formulas for 90, 180, and 270 degrees when the center is at the origin. The tutorial then introduces a method to handle rotations around a different center by shifting the graph to the origin, applying the rotation, and shifting it back. An example with a graph ABC is provided, demonstrating the calculation of interim points and the application of the rotation algorithm. The final rotated points are plotted to show the effect of rotating around a new center.

What are the basic angles for which we have simple rotation algorithms?

• 60, 120, 240 degrees

• 90, 180, 270 degrees

• 45, 90, 135 degrees

• 30, 60, 90 degrees

What is the first step when rotating an image around a point other than the origin?

• Rotate the image directly around the new point

• Move the entire graph to the origin

• Change the coordinates of the vertices

• Reflect the image across the x-axis

In the example, what is the new center of rotation?

• (1, 2)

• (2, 1)

• (-1, -2)

• (0, 0)

What do we do after moving the graph to the origin?

• Reflect the graph across the y-axis

• Scale the graph by a factor of 2

• Translate the graph back to its original position

• Perform the rotation using the origin rules

What is the final step after performing the rotation at the origin?

• Rotate the image again by 90 degrees

• Scale the image by a factor of 2

• Move the image back to its original position

• Reflect the image across the x-axis

What is the interim point for vertex A after shifting the graph?

• (-2, -3)

• (-4, -1)

• (-5, -4)

• (-6, -2)

What is the rule for a 90-degree rotation?

• Switch the sign of X and swap X and Y

• Swap X and Y without changing signs

• Switch the sign of both X and Y

• Switch the sign of Y and swap X and Y

What are the final coordinates of A' after the entire process?

• (2, -6)

• (4, -5)

• (0, -2)

• (-2, -4)

What is the purpose of drawing circles centered at the new rotation point?

• To translate the image

• To reflect the image

• To scale the image

• To verify the points are correctly placed

What is the final step to ensure the rotation is correct?

• Translate the image back to the origin

• Scale the image by a factor of 2

• Draw circles centered at the new rotation point

• Reflect the image across the y-axis