Translations, Reflections, and Rotations

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

Back

A translation can be represented as (x, y) → (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

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 the line of reflection?

Back

The line of reflection is the line over which a figure is reflected, and each point on the figure is equidistant from this line.

Front

How do you represent a reflection across the x-axis?

Back

A reflection across the x-axis can be represented as (x, y) → (x, -y).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation.

Front

How do you represent a 90-degree clockwise rotation?

Back

A 90-degree clockwise rotation can be represented as (x, y) → (y, -x).

Front

How do you represent a 90-degree counter-clockwise rotation?

Back

A 90-degree counter-clockwise rotation can be represented as (x, y) → (-y, x).

Front

What is the effect of a 180-degree rotation on a point (x, y)?

Back

A 180-degree rotation transforms the point (x, y) to (-x, -y).

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure without changing its orientation, while a reflection flips a figure over a line, changing its orientation.