Rotations and Reflections

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle in a specific direction.

Front

What is the rule for rotating a point (x,y) 90° counterclockwise around the origin?

Back

(x,y) → (-y,x)

Front

What is the rule for rotating a point (x,y) 180° around the origin?

Back

(x,y) → (-x,-y)

Front

What is the rule for rotating a point (x,y) 270° counterclockwise around the origin?

Back

(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

What is the rule for reflecting a point (x,y) over the x-axis?

Back

(x,y) → (x,-y)

Front

What is the rule for reflecting a point (x,y) over the y-axis?

Back

(x,y) → (-x,y)

Front

What is the rule for reflecting a point (x,y) over the line y = k?

Back

(x,y) → (x, 2k - y)

Front

How do you determine the image of a point after a 180° rotation around the origin?

Back

The image of a point (x,y) after a 180° rotation is (-x,-y).

Front

What happens to the coordinates of a point when it is reflected over the line x = k?

Back

The x-coordinate of the point changes to 2k - x, while the y-coordinate remains the same.