transformations in the coordinate plane

Front

What is a transformation in the coordinate plane?

Back

A transformation in the coordinate plane is a function that maps points from one location to another, altering their position, size, or orientation.

Front

What are the four main types of transformations?

Back

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

Front

Define translation in the context of transformations.

Back

Translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

What happens to the coordinates of a point during a translation of (x, y) → (x + a, y + b)?

Back

The x-coordinate is increased by 'a' and the y-coordinate is increased by 'b'.

Front

What is reflection in the coordinate plane?

Back

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

Front

How does reflecting a point across the y-axis affect its coordinates?

Back

Reflecting a point (x, y) across the y-axis results in the point (-x, y).

Front

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

Back

Reflecting a point (x, y) across the x-axis results in the point (x, -y).

Front

Define rotation in the context of transformations.

Back

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 result of a 90° counterclockwise rotation of the point (x, y)?

Back

The result is the point (-y, x).

Front

What is dilation in transformations?

Back

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