🕹️ Mission Control
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🔓 Distance Decryption System
Find absolute coordinate distance to disable lasers.
🕹️ Directional Step (1 Unit)
MOVE
🌀 Dimensional Axes Reflection
CERTIFICATE OF Cartesian MASTERY
Awarded to the Explorer of Grid Worlds
MASTER STUDENT
Having successfully demonstrated absolute-value calculation of distances on the 4-quadrant coordinate plane, and navigated barriers using axes reflections ($x$ and $y$ sign coordinate inversions) across all 3 Campaign Levels.
MISSION CONTROLLER:
Mr. Neft
Mr. Neft
EXPLORER SCORE:
24 Total Moves
24 Total Moves
📚 Cartesian Guidelines
Review the absolute value and coordinate mapping rules to solve missions quickly.
🪞 The Reflection Rules
- **Reflecting over the X-Axis**: The x-coordinate remains identical, but the y-coordinate sign flips to its opposite:
$$(x, y) \xrightarrow{\text{Reflect } X} (x, -y)$$
- **Reflecting over the Y-Axis**: The y-coordinate remains identical, but the x-coordinate sign flips to its opposite:
$$(x, y) \xrightarrow{\text{Reflect } Y} (-x, y)$$
📏 Coordinate Distances
To calculate the distance between two coordinates with matching x or y coordinates:
- **Different Quadrants**: Add the absolute values of the varying coordinates:
$$d = |y_1| + |y_2| \quad \text{or} \quad |x_1| + |x_2|$$
- **Same Quadrants**: Subtract the smaller absolute value from the larger:
$$d = |y_1| - |y_2| \quad \text{or} \quad |x_1| - |x_2|$$