Geometric transformations

Front

What is a geometric transformation?

Back

A geometric transformation is a function that moves or changes a shape in a specific way, such as translation, rotation, reflection, or dilation.

Front

What is translation in geometric transformations?

Back

Translation is a transformation that slides a figure from one position to another without turning it. It involves moving every point of the figure the same distance in the same direction.

Front

What is rotation in geometric transformations?

Back

Rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

What is reflection in geometric transformations?

Back

Reflection is a transformation that flips a figure over a line, creating a mirror image of the original figure.

Front

What is dilation in geometric transformations?

Back

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

Front

What is the scale factor in dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation.

Front

How do you represent a translation algebraically?

Back

A translation can be represented as (x, y) → (x + a, y + b), where 'a' and 'b' are the distances moved in the x and y directions, respectively.

Front

What is the algebraic representation for a reflection across the x-axis?

Back

The algebraic representation for a reflection across the x-axis is (x, y) → (x, -y).

Front

What is the algebraic representation for a reflection across the y-axis?

Back

The algebraic representation for a reflection across the y-axis is (x, y) → (-x, y).

Front

What is the algebraic representation for a rotation of 90 degrees counterclockwise around the origin?

Back

The algebraic representation for a rotation of 90 degrees counterclockwise around the origin is (x, y) → (-y, x).