Mission1: Rigid Transformations and Congruence

Explain rotation in the context of rigid transformations.

• Rotation is a rigid transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

• Rotation is a transformation that changes the size of a figure while keeping its shape.

• Rotation is a rigid transformation that flips a figure over a line, creating a mirror image.

• Rotation is a transformation that translates a figure from one location to another without changing its orientation.

What is the significance of the center of rotation?

• It is the point where all forces act on a figure.

• It is the fixed point around which a figure rotates; it determines the path and position of the rotated figure.

• It is the center of mass of the figure.

• It is the point where the figure's dimensions are measured from.

How can you determine if two shapes are congruent?

• By checking if they have the same area.

• By checking if one can be obtained from the other through a series of rigid transformations.

• By measuring their angles and ensuring they are equal.

• By comparing their colors and textures.

What is the angle of rotation in a full turn?

• 180 degrees

• 360 degrees

• 90 degrees

• 270 degrees

What does it mean to translate a trapezoid?

• To rotate the trapezoid around a point.

• To change the size of the trapezoid.

• To move it to a different location on the plane without changing its shape or size.

• To flip the trapezoid over a line.

What happens to the coordinates of a point after a reflection across the x-axis?

• The coordinates change to (x, y)

• The coordinates change to (-x, y)

• The coordinates change to (x, -y)

• The coordinates remain the same

What is the rule for reflection across the y-axis?

• Each point (x, y) is transformed to (-x, y).

• Each point (x, y) is transformed to (x, -y).

• Each point (x, y) is transformed to (-y, x).

• Each point (x, y) is transformed to (y, x).

What is a reflection in geometry?

• A transformation that enlarges a figure

• A rigid transformation that flips a figure over a line, creating a mirror image.

• A process of rotating a figure around a point

• A method of translating a figure to a different location

What is the difference between rotation and dilation?

• Rotation is a transformation that changes the size of a shape, while dilation changes its position.

• Rotation is a rigid transformation that changes the position of a shape without altering its size, while dilation changes the size of a shape but not its shape.

• Rotation and dilation are the same transformations that only affect the shape's color.

• Dilation is a transformation that only applies to three-dimensional shapes, while rotation applies to two-dimensional shapes.

How do you identify the direction of rotation?

• By observing the movement of the figure

• By measuring the angle of rotation

• By the color of the object

• By the size of the object