Reflection Game

Reflection Game
Welcome to Reflection Rift! This is a geometry-based puzzle game where you practice reflecting points and shapes across different lines on a coordinate plane. Scroll down the page for a more detailed explanation.
 

 

How to Play the Reflection Game
The Objective
Your mission is to find the new coordinates of a “ship” (a point or a triangle) after it has been flipped over a mirror line. You must complete 10 trials to finish the mission.
Game Modes
Mirror Basic (Axis Mastery): You will reflect points across the x-axis (the horizontal line) or the y-axis (the vertical line).
Mirror Advanced (Diagonal Shift): You will reflect points across the diagonal line y = x.
Mirror Tactical (Fleet Mirage): You analyze an entire triangle “fleet” being reflected.

How to Play

1. Analyze the Mirror Line
   Look at the grid on the screen. The game will highlight the “mirror” in dashed pink.
   Horizontal Line: x-axis
   Vertical Line: y-axis
   Diagonal Line: y = x
   

2. Locate the Original Ship
   The starting position is shown as a grey dashed point or triangle. Below the grid, the “Original Point” coordinates are displayed—for example, (3, -2).
   

3. Calculate the Reflection
   Based on the mirror line, determine where the ship would “land” if it flipped over that line.
   

4. Select your Answer
   Click one of the four coordinate options at the bottom.
   Correct: The button turns blue, the message “MIRROR SYNCED” appears, and the solid pink reflected ship is revealed on the grid.
   Incorrect: The button turns red, and the message “IMAGE DISTORTED” appears.
   

5. Proceed
   Click the “NEXT RIFT ➜” button to move to the next of your 10 trials.
   

The “Cheat Sheet” Rules
To master the game, remember these three mathematical shortcuts:

Mirror Line	Original Point	Reflected Point	What Happens?
x-axis	(x, y)	(x, -y)	The y value changes sign (Up becomes Down).
y-axis	(x, y)	(-x, y)	The x value changes sign (Left becomes Right).
y = x	(x, y)	(y, x)	The x and y values swap places.

Reflecting on the Coordinate Plane
Key Characteristics
Perpendicular Distance: The line of reflection is the perpendicular bisector of the segment connecting any point and its reflected image.
Isometry: Reflections are “rigid motions.” The size and shape of the object do not change; the image is congruent to the pre-image.
Opposite Orientation: Unlike translations (slides), reflections change the orientation of an object. A right hand reflected in a mirror looks like a left hand.

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

• Show Video

 

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