Exploring Transformations and Rotations in Geometry

Miss Smith's math tutorial covers the concept of rotations as a type of transformation. The video explains different types of rotations, including 90 degrees counterclockwise, 180 degrees, and 270 degrees counterclockwise, and provides rules for each. Practical examples are used to demonstrate these rotations, and students are given an exercise to practice rotating points 180 degrees.

What is the transformation rule for rotating a point 90 degrees counterclockwise?

• X, Y becomes Y, -X

• X, Y becomes Y, X

• X, Y becomes -Y, X

• X, Y becomes -X, -Y

Which of the following is equivalent to a 90 degrees counterclockwise rotation?

• 180 degrees clockwise

• 360 degrees clockwise

• 90 degrees clockwise

• 270 degrees clockwise

What happens to the coordinates of a point when it is rotated 180 degrees?

• X, Y remains X, Y

• X, Y becomes -X, -Y

• X, Y becomes -Y, -X

• X, Y becomes Y, X

What is the transformation rule for a 180 degrees rotation?

• X, Y becomes Y, -X

• X, Y becomes -X, -Y

• X, Y becomes -Y, -X

• X, Y becomes Y, X

A rotation of 270 degrees counterclockwise is the same as rotating:

• 90 degrees clockwise

• 90 degrees counterclockwise

• 180 degrees counterclockwise

• 270 degrees clockwise

Which transformation rule applies when rotating a point 270 degrees counterclockwise?

• X, Y becomes Y, X

• X, Y becomes -Y, X

• X, Y becomes Y, -X

• X, Y becomes -X, -Y

If a point is at (4, 2) and undergoes a 90 degrees counterclockwise rotation, what will be its new coordinates?

• (2, 4)

• (-2, 4)

• (4, -2)

• (-4, 2)

What is the result of rotating a point 180 degrees, regardless of the direction of rotation?

• The point's coordinates swap places

• The point moves to a new quadrant

• The point's coordinates are both negated

• The point returns to its original position

Which statement is true about the rotation of points in geometry?

• Rotation does not change the point's location

• Rotation can only be performed clockwise

• All rotations result in the point returning to its original position

• Rotation changes the point's coordinates according to specific rules

After rotating a point (1, 2) by 270 degrees counterclockwise, what are the new coordinates?

• (-1, 2)

• (2, -1)

• (-2, 1)

• (1, -2)