Transformations Review

Front

What is a transformation in geometry?

Back

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

Front

Define reflection in geometry.

Back

Reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

What is the line of reflection for a reflection across the y-axis?

Back

The line of reflection is the y-axis itself, where each point (x, y) is transformed to (-x, y).

Front

How do you reflect a point over the line y = -x?

Back

To reflect a point (a, b) over the line y = -x, switch the coordinates and change their signs: (a, b) becomes (-b, -a).

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in the same direction.

Front

How do you translate a point by a vector?

Back

To translate a point (x, y) by a vector , add the vector components to the point: (x + a, y + b).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation.

Front

How do you rotate a point 90 degrees counterclockwise around the origin?

Back

To rotate a point (x, y) 90 degrees counterclockwise, the new coordinates become (-y, x).

Front

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

Back

A 180-degree rotation transforms a point (x, y) to (-x, -y).

Front

What is the difference between clockwise and counterclockwise rotation?

Back

Clockwise rotation moves in the direction of a clock's hands, while counterclockwise rotation moves in the opposite direction.