Rotating Points and Quadrants

Front

What is the definition of rotation in geometry?

Back

Rotation in geometry refers to turning a figure around a fixed point, known as the center of rotation, by a certain angle in a specific direction.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What are the four quadrants in a Cartesian coordinate system?

Back

The four quadrants are: Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), Quadrant IV (x > 0, y < 0).

Tags

CCSS.6.NS.C.6B

Front

What is the rule for rotating a point 90° clockwise?

Back

The rule for rotating a point (x, y) 90° clockwise is (x, y) → (y, -x).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the rule for rotating a point 180° clockwise?

Back

The rule for rotating a point (x, y) 180° clockwise is (x, y) → (-x, -y).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the rule for rotating a point 270° clockwise?

Back

The rule for rotating a point (x, y) 270° clockwise is (x, y) → (-y, x).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the rule for rotating a point 90° counterclockwise?

Back

The rule for rotating a point (x, y) 90° counterclockwise is (x, y) → (-y, x).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the rule for rotating a point 180° counterclockwise?

Back

The rule for rotating a point (x, y) 180° counterclockwise is (x, y) → (-x, -y).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the rule for rotating a point 270° counterclockwise?

Back

The rule for rotating a point (x, y) 270° counterclockwise is (x, y) → (y, -x).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

How does the direction of rotation affect the coordinates of a point?

Back

The direction of rotation (clockwise or counterclockwise) determines how the coordinates of a point change based on the rotation angle.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the significance of the origin in rotations?

Back

The origin (0, 0) is often used as the center of rotation, meaning all rotations are performed around this fixed point.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5