Transformation of figures onto itself

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 main types of transformations?

Back

The main types of transformations are translations, rotations, reflections, and dilations.

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, by a certain angle.

Front

What is a reflection in geometry?

Back

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

Front

What is a translation in geometry?

Back

A translation is a transformation that slides a figure from one position to another without changing its shape or orientation.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, by a scale factor.

Front

What does it mean for a figure to map onto itself?

Back

A figure maps onto itself when a transformation is applied, and the resulting image is identical to the original figure.

Front

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

Back

A 180-degree rotation about the center point of a rectangle will map the rectangle onto itself.

Front

How does a reflection across the y-axis affect a regular pentagon?

Back

A reflection across the y-axis will map a regular pentagon onto itself, as it has symmetry along that axis.

Front

What is the significance of the blue line in transformations?

Back

The blue line represents the line of reflection; reflecting a trapezoid across this line will map it onto itself.