Transformations and Symmetry

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

Front

Define translation in the context of transformations.

Back

Translation is a type of transformation that slides a figure in a straight line from one position to another without changing its size, shape, or orientation.

Front

What does it mean to reflect a shape?

Back

Reflection is a transformation that flips a shape over a line, creating a mirror image.

Front

What is rotation in geometry?

Back

Rotation is a transformation that turns a shape around a fixed point, known as the center of rotation, by a certain angle.

Front

How do you determine the new coordinates of a point after a translation?

Back

To find the new coordinates, add the translation values to the original coordinates. For example, translating point (x,y) by (a,b) results in (x+a, y+b).

Front

What is the angle of rotation for a 90° counterclockwise rotation?

Back

A 90° counterclockwise rotation moves a point (x,y) to (-y,x).

Front

What is the angle of rotation for a 180° rotation?

Back

A 180° rotation moves a point (x,y) to (-x,-y).

Front

What is the angle of rotation for a 270° counterclockwise rotation?

Back

A 270° counterclockwise rotation moves a point (x,y) to (y,-x).

Front

What is symmetry in geometry?

Back

Symmetry is a property where a shape is invariant under certain transformations, such as reflection or rotation.

Front

What is the line of symmetry?

Back

The line of symmetry is a line that divides a shape into two identical parts that are mirror images of each other.