Transformations

Front

What is a transformation in geometry?

Back

A transformation is a mathematical operation that moves or changes a shape in some way, including translations, rotations, reflections, and dilations.

Front

Define translation in geometry.

Back

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

Front

What is reflection in geometry?

Back

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

Front

Explain rotation in geometry.

Back

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

Front

What is dilation in geometry?

Back

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

Front

How do you reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate to get (-x, y).

Front

What is the rule for translating a point (x, y) by (2, -1)?

Back

The rule for this translation is (x + 2, y - 1).

Front

What happens to the coordinates of a point when it is rotated 90° counterclockwise about the origin?

Back

The coordinates (x, y) become (-y, x) after a 90° counterclockwise rotation.

Front

What is the effect of a 180° rotation on a point (x, y)?

Back

A 180° rotation changes the coordinates (x, y) to (-x, -y).

Front

How do you perform a 270° clockwise rotation on a point (x, y)?

Back

A 270° clockwise rotation changes the coordinates (x, y) to (y, -x).