Transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape to create a new shape. Common types include translations, rotations, reflections, and dilations.

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 does it mean to reflect a point across the y-axis?

Back

To reflect a point (x, y) across the y-axis, the x-coordinate changes sign, resulting in the point (-x, y).

Front

What does it mean to rotate a point 180 degrees about the origin?

Back

To rotate a point (x, y) 180 degrees about the origin, both coordinates change sign, resulting in the point (-x, -y).

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, size, or orientation.

Front

How do you identify a translation from one point to another?

Back

A translation can be identified by the change in coordinates, expressed as (x + a, y + b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

What is the effect of reflecting a point across the x-axis?

Back

Reflecting a point (x, y) across the x-axis changes the sign of the y-coordinate, resulting in the point (x, -y).

Front

What is the general rule for translating a point (x, y) by (h, k)?

Back

The new coordinates after translation are (x + h, y + k).

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, by a specified angle.

Front

What is the effect of a 90-degree clockwise rotation on a point (x, y)?

Back

A 90-degree clockwise rotation transforms the point (x, y) to (y, -x).