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. Common types include translations, rotations, reflections, and dilations.

Front

What is a translation?

Back

A translation is a type of transformation that slides a figure in a straight line from one position to another without changing its size, shape, or orientation.

Front

What is a rotation?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle in a specific direction.

Front

What is a reflection?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image of the original figure.

Front

What is the notation for a translation of (x, y) by (a, b)?

Back

The notation for a translation of (x, y) by (a, b) is (x + a, y + b).

Front

What does it mean to rotate a point 90 degrees clockwise about the origin?

Back

To rotate a point 90 degrees clockwise about the origin, you switch the coordinates and change the sign of the new x-coordinate. For example, (x, y) becomes (y, -x).

Front

What is the result of reflecting a point (x, y) over the x-axis?

Back

The result of reflecting a point (x, y) over the x-axis is (x, -y).

Front

What is the result of reflecting a point (x, y) over the y-axis?

Back

The result of reflecting a point (x, y) over the y-axis is (-x, y).

Front

What is the result of reflecting a point (x, y) over the line y = x?

Back

The result of reflecting a point (x, y) over the line y = x is (y, x).

Front

What is the composition of transformations?

Back

The composition of transformations is the application of two or more transformations in sequence, where the output of one transformation becomes the input for the next.