Rotation Game

Rotation Game
Welcome to Rotation Radius! This game is designed to help you master coordinate geometry by rotating objects around the center of the grid (the origin). Scroll down the page for a more detailed explanation.
 

 

How to Play the Rotation Game
Your Mission
You must calculate where a point or a “fleet” (triangle) will land after being rotated by a specific angle. You have 10 trials to complete your flight path.

Mission Modes
Orbital Basic: Practice single-point rotations of 90° (both clockwise and counter-clockwise).
Orbital Advanced: Focus specifically on 180° “Deep Space Flips."
Orbital Tactical: Calculate the new coordinates for an entire triangular squadron.

How to Play

1. Identify the Target
   When a level starts, look at the grey dashed point on the grid. This is your starting position. The exact coordinates, such as (2, 3), will be listed in the “Origin Point” info box.
   

2. Check the Rotation Angle
   Look at the Orbit Angle display or the text below the grid. It will tell you the required maneuver:
   90° Counter-Clockwise: A quarter-turn to the left.
   90° Clockwise: A quarter-turn to the right.
   180° Turn: A half-circle turn (lands in the opposite quadrant).
   

3. Use the Orbital Ring
   Notice the faint, dashed circle on the grid? That is your Orbit Line. The point must stay on this circle; it only slides along the perimeter to a new position.
   

4. Select the Coordinates
   Choose the correct resulting coordinate from the four buttons at the bottom.
   Correct: The button glows violet, you’ll see “ORBIT STABILIZED”, and the final solid violet shape appears.
   Incorrect: The button turns red, and you’ll see “NAVIGATION FAILURE”.
   

The “Cheat Sheet” Rules
To master the game, remember these three mathematical shortcuts for a point (x, y)::

Rotation	New Coordinates	Pro Tip
90° Counter-Clockwise	(-y, x)	Swap x and y, make the new x negative.
90° Clockwise	(y, -x)	Swap x and y, make the new y negative.
180° Turn	(-x, -y)	Keep them in place, just flip both signs (+ to -).
270° Counter-Clockwise	(y, -x)	Same as 90° clockwise.
270° Clockwise	(-y, x)	Same as 90° counter-clockwise.

Rotation on the Coordinate Plane
A rotation is defined by two things:
The Angle: How far you turn (usually 90°, 180°, or 270°).
The Direction: Clockwise or Counter-Clockwise.

How to Rotate a Shape
If you are rotating a full shape (like a triangle) instead of just one point, follow these steps:
Identify the vertices: Write down the coordinates for every corner of the shape.
Apply the rule: Use the table above to transform each coordinate.
Plot the new points: Draw the new vertices on the grid.
Connect the dots: The resulting shape should be identical in size and shape to the original, just “turned.”

The video gives a clear, step-by-step approach to learn rotation on the coordinate plane.

• Show Video

 

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