Geometry Transformations

Front

What is a transformation in geometry?

Back

A transformation in geometry is an operation that moves or changes a shape in some way, such as translation, rotation, reflection, or dilation.

Front

What is the notation for a reflection over the y-axis?

Back

The notation for a reflection over the y-axis is R_{y axis}.

Front

How do you describe a translation mathematically?

Back

A translation can be described using the formula (x + a, y + b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

What is the result of reflecting a point (x, y) over the y-axis?

Back

The result of reflecting a point (x, y) over the y-axis is (-x, y).

Front

What is the result of reflecting a point (x, y) over the x-axis?

Back

The result of reflecting a point (x, y) over the x-axis is (x, -y).

Front

What is the effect of a 360-degree rotation on a point?

Back

A 360-degree rotation about a point returns the point to its original position.

Front

What is the line of reflection for the points (2, -7) and (-7, 2)?

Back

The line of reflection for the points (2, -7) and (-7, 2) is y = x.

Front

How do you perform a translation from Point A (3, -8) to A'(-4, -5)?

Back

To translate Point A (3, -8) to A'(-4, -5), you subtract 7 from the x-coordinate and add 3 to the y-coordinate, resulting in the translation (x - 7, y + 3).

Front

What is the general formula for a rotation of 90 degrees counterclockwise about the origin?

Back

The general formula for a rotation of 90 degrees counterclockwise about the origin is (x, y) -> (-y, x).

Front

What is the general formula for a rotation of 180 degrees about the origin?

Back

The general formula for a rotation of 180 degrees about the origin is (x, y) -> (-x, -y).