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 happens to the coordinates of a point (x, y) when it is rotated 180° about the origin?

Back

The coordinates change to (-x, -y).

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 happens to the y-coordinate of a point when it is reflected over the x-axis?

Back

The y-coordinate changes sign, becoming -y.

Front

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

Back

The rule is (x, y) → (y, -x).

Front

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

Back

The rule is (x, y) → (-y, x).

Front

If triangle ABC is reflected over the line y = x, what happens to the coordinates of point A (x, y)?

Back

The coordinates change to (y, x).

Front

What is the effect of a reflection over the y-axis on the coordinates of a point (x, y)?

Back

The x-coordinate changes sign, becoming (-x, y).

Front

What is the center of rotation?

Back

The center of rotation is the fixed point around which a figure is rotated.

Front

How do you determine the new coordinates of a point after a 90° counterclockwise rotation?

Back

Use the rule (x, y) → (-y, x).