Rotation Around Origin Calculator

Frequently Asked Questions

What is rotation in geometry?

Rotation is a transformation that turns a point around a center (usually origin) by an angle. All points rotate the same amount. Distances and angles are preserved.

How do I rotate 90° counterclockwise?

Use formula: (x,y) → (-y,x). Point (3,4) becomes (-4,3). Positive angles rotate counterclockwise.

How do I rotate 180°?

Use formula: (x,y) → (-x,-y). Point (3,4) becomes (-3,-4). Opposite side of origin, same distance.

How do I rotate 270° counterclockwise?

Equivalent to -90° or 90° clockwise. Formula: (x,y) → (y,-x). Point (3,4) becomes (4,-3).

What is clockwise vs counterclockwise rotation?

Counterclockwise: positive angle. Clockwise: negative angle. 90° counterclockwise = -270° clockwise. Standard convention uses counterclockwise as positive.

Does rotation preserve distance?

Yes. Rotation is an isometry. All distances from origin stay the same, angles stay the same, shape unchanged.

Does rotation change the shape?

No. Rotation preserves all distances and angles. A triangle rotated stays congruent. Only position and orientation change.

What is the center of rotation?

The point around which everything rotates. Standard is origin (0,0). Rotating around other centers requires translation.

How do I rotate a polygon?

Apply rotation formula to each vertex separately. Connect reflected vertices. All vertices rotate by same angle.

What is the difference between rotation and reflection?

Rotation: turns around point, preserves orientation (clockwise stays clockwise). Reflection: flips across line, reverses orientation.

Can I rotate by angles other than 90/180/270?

Yes, but requires trigonometry: x'=x·cos(θ)-y·sin(θ), y'=x·sin(θ)+y·cos(θ). Standard geometry focuses on 90° multiples.

How are rotations composed?

Multiple rotations add angles. Two 90° rotations = 180° rotation. 90°+180°+90°=360°=no change (identity).