Transformations

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

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

What does translation mean in geometry?

Back

Translation means moving a shape from one location to another without changing its size, shape, or orientation.

Front

How do you describe a translation mathematically?

Back

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

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a shape 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 shape is reflected, and each point on the shape is equidistant from this line.

Front

What does rotation mean in geometry?

Back

Rotation means turning a shape around a fixed point, known as the center of rotation, by a certain angle.

Front

How do you describe a rotation mathematically?

Back

A rotation can be described using the notation (x, y) → (x', y'), where (x', y') are the new coordinates after rotating by an angle θ around a point.

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a shape but keeps its proportions the same.

Front

How do you describe a dilation mathematically?

Back

A dilation can be described using the notation (x, y) → (kx, ky), where 'k' is the scale factor.