Warm up: Compositions of Transformations

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 shape from one position to another without turning it. The shape remains congruent to the original.

Front

What is a rotation?

Back

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

Front

What is a reflection?

Back

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

Front

What is the line of reflection?

Back

The line of reflection is the line over which a shape is reflected. Each point of the original shape is the same distance from the line as the corresponding point in the reflected shape.

Front

What is a composition of transformations?

Back

A composition of transformations is when two or more transformations are combined to produce a single transformation.

Front

What is the effect of reflecting a shape over the x-axis?

Back

Reflecting a shape over the x-axis changes the sign of the y-coordinates of the points in the shape.

Front

What is the effect of reflecting a shape over the y-axis?

Back

Reflecting a shape over the y-axis changes the sign of the x-coordinates of the points in the shape.

Front

What is the order of transformations?

Back

The order of transformations matters because performing them in different sequences can lead to different results.

Front

What is the result of rotating a shape 90 degrees clockwise?

Back

Rotating a shape 90 degrees clockwise around the origin transforms the coordinates (x, y) to (y, -x).