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The image shows a mathematical question about a translation rule: \((x, y) \rightarrow (x + 2, y - 4)\). The problem asks to determine how this rule represents a translation in terms of units in specific directions.

1. The rule \((x, y) \rightarrow (x + 2, y - 4)\) means:
   - \(x + 2\): The x-coordinate is increased by 2 units, so this represents a translation **2 units to the right**.
   - \(y - 4\): The y-coordinate is decreased by 4 units, so this represents a translation **4 units down**.

The correct answer would be: **2 units right** and **4 units down**.

Would you like more details or clarification on this? 

Here are 5 related questions:
1. How do you translate a point 5 units to the left and 3 units up?
2. What is the effect of translating a point \( (x, y) \) by \( (x + a, y + b) \)?
3. How does translation affect the distance between points?
4. What is the difference between translation and rotation in geometry?
5. How would you write the translation rule for moving a point 6 units down and 7 units to the left?

**Tip:** Translations preserve the shape and size of geometric figures; they only shift the position.

The rule (x, y) -> (x + 2, y - 4) represents a translation 2 units right and 4 units down.

Learn how the translation rule (x + 2, y - 4) shifts a point 2 units to the right and 4 units down in coordinate geometry. Suitable for students in Grades 6-8, this problem covers essential concepts of translations and their effects.

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