Transformations and Rotations in Geometry

Front

What is a transformation in geometry?

Back

A transformation in geometry is an operation that moves or changes a shape in some way to produce a new shape, called the image.

Front

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

Define rotation in geometry.

Back

Rotation is a transformation that turns a figure about a fixed point at a given angle and in a specified direction.

Front

What is the result of rotating a point (x, y) 180° about the origin?

Back

The result is (-x, -y).

Front

If point A is at (3, 4), what are the coordinates of A' after a 90° counterclockwise rotation about the origin?

Back

The coordinates of A' would be (-4, 3).

Front

What is the image of a figure?

Back

The image of a figure is the new figure that results from a transformation.

Front

What does it mean to reflect a figure over the x-axis?

Back

To reflect a figure over the x-axis means to flip it over the x-axis, changing the sign of the y-coordinates.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90° angle.

Front

If a figure is translated 5 units to the right and 3 units up, how do the coordinates change?

Back

If a point (x, y) is translated, the new coordinates will be (x + 5, y + 3).

Front

What is the difference between a rotation and a reflection?

Back

A rotation turns a figure around a point, while a reflection flips a figure over a line.