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 reflection transformation?

Back

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

Front

What is a rotation transformation?

Back

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

Front

What is a translation transformation?

Back

A translation transformation slides a shape in a straight line from one position to another without changing its size or orientation.

Front

What is a dilation transformation?

Back

A dilation transformation resizes a shape by a scale factor relative to a fixed point, either enlarging or reducing it.

Front

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

Back

For a figure to map onto itself means that after a transformation, the figure remains unchanged in appearance.

Front

What is the significance of the y-axis in transformations?

Back

The y-axis can be used as a line of reflection, meaning shapes can be flipped over this axis to create a mirror image.

Front

How does a 180-degree rotation affect a rectangle?

Back

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

Front

What is the effect of reflecting a trapezoid across a specific line?

Back

Reflecting a trapezoid across a specific line can map the trapezoid onto itself if the line is a line of symmetry.