Sequence of Transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape to create a new shape. Common transformations include translations, rotations, reflections, and dilations.

Front

Define translation in the context of transformations.

Back

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

Front

What is a reflection in geometry?

Back

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

Front

Explain rotation in terms of geometric transformations.

Back

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

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a shape but not its shape, by a scale factor relative to a center point.

Front

What does it mean to map one shape onto another?

Back

To map one shape onto another means to apply a sequence of transformations that will move the first shape to coincide with the second shape.

Front

What is the sequence of transformations?

Back

The sequence of transformations refers to the specific order in which multiple transformations are applied to a shape.

Front

How does the order of transformations affect the final image?

Back

The order of transformations can significantly affect the final image; different sequences can lead to different results.

Front

What is the effect of a 90° clockwise rotation on a point (x, y)?

Back

A 90° clockwise rotation transforms the point (x, y) to (y, -x).

Front

What is the effect of a reflection over the x-axis on a point (x, y)?

Back

A reflection over the x-axis transforms the point (x, y) to (x, -y).