Exploring Rotations on the Coordinate Plane

This video tutorial covers rotations on the coordinate plane, explaining how to rotate figures around a center of rotation to create congruent images. It discusses the degrees of rotation (90, 180, 270, 360) and the importance of direction (clockwise and counterclockwise). The tutorial includes examples and exercises to help understand the concept, and it highlights patterns in rotations, such as changes in coordinates. The lesson concludes with a summary of key points and encourages viewers to apply what they've learned.

What is the center of rotation typically used in coordinate plane rotations?

• The origin (0,0)

• The point (1,1)

• The top-left corner of the plane

• The center of the figure being rotated

How many degrees does a full rotation around the origin encompass?

• 180 degrees

• 90 degrees

• 360 degrees

• 270 degrees

What does a 270-degree rotation typically result in on the coordinate plane?

• A quarter turn clockwise

• A half turn

• Three quarters of a turn clockwise

• A full turn

Which direction does a clockwise rotation move on the coordinate plane?

• Right to left

• Left to right

• Top to bottom

• Bottom to top

If a figure starts in quadrant one and after rotation ends up in quadrant four, how many degrees was it rotated?

• 360 degrees clockwise

• 270 degrees clockwise

• 180 degrees clockwise

• 90 degrees clockwise

What does a counterclockwise rotation imply on the coordinate plane?

• Movement in the direction opposite to a clock's hands

• Movement in the direction of a clock's hands

• No movement

• Random movement

What is the algebraic representation for a 180-degree rotation on the coordinate plane?

• (x, y) to (-x, -y)

• (x, y) to (y, -x)

• (x, y) to (x, y)

• (x, y) to (-y, x)

How does a 90-degree clockwise rotation affect the coordinates of a point?

• (x, y) to (y, -x)

• (x, y) to (-y, x)

• (x, y) to (x, y)

• (x, y) to (-x, -y)

What is the result of a 270-degree counterclockwise rotation algebraically represented as?

• (x, y) to (-x, -y)

• (x, y) to (-y, x)

• (x, y) to (x, y)

• (x, y) to (y, -x)

If a point rotates 360 degrees, what happens to its position?

• It moves to the opposite quadrant

• It returns to its original position

• It moves to an adjacent quadrant

• It disappears from the plane