Translation Game

Translation Game
Welcome to Warp Trials, an interstellar math game designed to test your mastery of coordinate geometry and translations. In this game, you take on the role of a Coordinate Cadet. Your mission is to navigate “sectors” by correctly identifying or applying mathematical rules to move ships (points and shapes) across a 2D grid. Scroll down the page for a more detailed explanation.
 

 

How to Play the Translation Game
Game Modes
You can choose to focus on a specific skill or test your versatility in the “Elite” mixed mode:
Execution (Apply Warp Rule): You are given a starting point and a rule like (x+2, y-3). You must calculate the final (x, y) coordinates of the destination.
Analysis (Identify the Rule): You see a ship’s original position (ghost ship) and its new position. You must identify the specific translation rule used to move it.
Tactical (Fleet Maneuvers): Instead of a single point, you must analyze how an entire triangle (a “fleet”) moved across the grid.
Elite (Mixed Trials): A random rotation of all three modes.

How to Play

1. Select Your Mission
   On the main menu, click on one of the Mission Type cards to begin your trial. Each session consists of 10 trials.
   

2. Analyze the Grid
   The Ghost Ship: A grey, dashed outline representing the Origin (starting position).
   The Active Ship: A solid purple shape representing the Destination (final position).
   Note: In “Execution” mode, the purple ship only appears after you select the correct answer.
   

3. Choose the Correct Warp
   Look at the Options Container (the four buttons below the grid).
   If the prompt says “Calculate Destination,” pick the button with the correct (x, y) coordinates.
   If the prompt says “Identify Warp Rule,” pick the button that shows the correct horizontal and vertical change, such as (x-4, y+2).
   

4. Progress and Feedback
   Success: The button turns deep blue, and you’ll see WARP SUCCESSFUL.
   Error: The button turns red, and you’ll see CALCULATION ERROR.
   Click PROCEED to move to the next trial. Use the progress bar at the top to track your journey.
   

Translating on the Coordinate Plane
In geometry, translation is a type of transformation that slides a figure in any direction without rotating it, resizing it, or flipping it. Think of it as “nudging” an object across a surface. On a coordinate plane, every point (x, y) of a figure is moved by the exact same distance in a horizontal and/or vertical direction.

The Mapping Rule
Translations are described using a mathematical rule. If you want to move a point h units horizontally and k units vertically, the rule is written as:
(x, y) → (x + h, y + k)
Horizontal shift (h): If h is positive, the object moves right. If h is negative, it moves left.
Vertical shift (k): If k is positive, the object moves up. If k is negative, it moves down.

Properties of Translation
When you translate a shape, certain things stay the same and others change:
Isometry: The original shape (the Pre-image) and the new shape (the Image) are congruent. This means they have the same side lengths, angles, and area.
Orientation: The shape still “faces” the same way. If a triangle’s tip is pointing up before the translation, it will still point up afterward.
Parallelism: The segments connecting the corresponding vertices of the Pre-image and the Image are parallel to each other.

Step-by-Step Example
Imagine you have a point A located at (2, 3) and you are given the rule (x - 4, y + 2)
Identify the shifts: We are moving 4 units left (because of -4) and 2 units up (because of +2).
Apply to x: 2 - 4 = -2
Apply to y: 3 + 2 = 5
Final Result: The new point A’ (pronounced “A-prime”) is located at (-2, 5).

Translating Whole Shapes
To translate a polygon, you simply apply the rule to every vertex (corner) of the shape and then connect the new points.
If you have a triangle with vertices at (1,1), (3,1), and (2,3), and you translate it by (x+5, y+0), the entire triangle “slides” 5 units to the right, maintaining its exact shape and size.

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

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.