Rotating Points and Coordinates

This video tutorial explains how to rotate a point about a new center, not the origin. It covers three examples: rotating a point 90, 180, and 270 degrees counterclockwise. The tutorial also explains the origin of these rotation rules, providing a deeper understanding of the concepts. The video concludes with a call to explore further resources and support the channel.

What is the main focus of this lesson?

• Rotating a point about a non-origin center

• Reflecting a point

• Rotating a point about the origin

• Translating a point

What is the first step in the three-step rotation process?

• Add the center of rotation to the point

• Reflect the point across the x-axis

• Translate the point

• Subtract the center of rotation from the point

In the first example, what is the initial point being rotated?

• (2, 5)

• (1, 3)

• (0, 2)

• (3, 1)

What is the result of rotating the point (2, 5) 90 degrees counterclockwise about (1, 3)?

• (-1, 4)

• (1, 2)

• (0, 3)

• (-2, 1)

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

• (1, 3)

• (3, 0)

• (0, 2)

• (2, 5)

What is the result of rotating the point (1, -4) 180 degrees?

• (-1, 6)

• (1, 4)

• (-1, -6)

• (0, 2)

In the third example, what is the point being rotated?

• (2, 5)

• (1, -4)

• (0, 2)

• (-2, -5)

What is the result of rotating the point (-2, -5) 270 degrees counterclockwise about (-1, 2)?

• (-8, 3)

• (0, 2)

• (1, -4)

• (-7, 1)

What happens to the coordinates when a point is rotated 90 degrees?

• X and Y switch, new X is opposite

• X and Y switch, new Y is opposite

• X and Y remain the same

• Only X changes

What is the effect of a 180-degree rotation on a point's coordinates?

• Only X changes

• Coordinates become opposite

• Coordinates remain the same

• Coordinates switch places