Transformational Geometry-Reflections and Translation

Front

What is transformational geometry?

Back

Transformational geometry is a branch of geometry that studies the properties of figures that are invariant under certain transformations, such as translations, rotations, reflections, and dilations.

Front

What is a translation in geometry?

Back

A translation is a type of transformation that moves every point of a figure a constant distance in a specified direction.

Front

How do you describe a translation?

Back

A translation can be described by specifying the direction and distance each point of the figure moves.

Front

What is a reflection in geometry?

Back

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

Front

What happens to the coordinates of a point when it is reflected over the y-axis?

Back

When a point (x, y) is reflected over the y-axis, its coordinates change to (-x, y).

Front

What is the effect of translating a figure 5 units to the right and 8 units down?

Back

The new coordinates of each point of the figure will be obtained by adding 5 to the x-coordinate and subtracting 8 from the y-coordinate.

Front

What is the relationship between translations and slides?

Back

A slide is another term for a translation; both refer to the same geometric transformation.

Front

How do you reflect a figure over the x-axis?

Back

To reflect a figure over the x-axis, the y-coordinates of each point are multiplied by -1, changing (x, y) to (x, -y).

Front

What is the general rule for reflecting a point across the line y = x?

Back

When reflecting a point (x, y) across the line y = x, the coordinates are swapped, resulting in (y, x).

Front

What is the significance of the origin in transformations?

Back

The origin (0, 0) serves as a reference point for many transformations, particularly rotations and reflections.