Geometric Transformations

Front

What is a geometric transformation?

Back

A geometric transformation is a function that maps a set of points in a plane to another set of points, altering the position, size, or orientation of the figure.

Front

What are the four main types of geometric transformations?

Back

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

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified 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 rotation in geometry?

Back

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

Front

What are the rotation rules for a 90° clockwise rotation?

Back

The rotation rule for a 90° clockwise rotation is (x, y) → (y, -x).

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

How do you find the coordinates of a point after reflection across the x-axis?

Back

To find the coordinates after reflection across the x-axis, change the sign of the y-coordinate: (x, y) → (x, -y).

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Front

How do you represent a dilation mathematically?

Back

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