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Eric used the diagram below to translate ABCD parallelogram to a notation of

(x,y)--> (x+6, y-3).  Is he correct? 



Responses

Yes, he is correct
Yes, he is correct

No, translation should be (x,y)--> (x+3, y-6))
No, translation should be (x,y)--> (x+3, y-6))

No, translation should be (x,y)--> (x-3, y+6)
No, translation should be (x,y)--> (x-3, y+6)

No, translation should be (x,y)--> (x-6, y+3)

Looking at the diagram, it shows the original parallelogram \( ABCD \) and its translated image \( A'B'C'D' \). To determine whether Eric's translation is correct, we can analyze the shift in both the \( x \)- and \( y \)-coordinates from \( ABCD \) to \( A'B'C'D' \).

- The points of parallelogram \( ABCD \) in quadrant I are:
  - \( A(1, -1) \)
  - \( B(4, -1) \)
  - \( C(4, 2) \)
  - \( D(1, 2) \)

- The points of the translated parallelogram \( A'B'C'D' \) in quadrant II are:
  - \( A'(-3, 5) \)
  - \( B'(-6, 5) \)
  - \( C'(-6, 2) \)
  - \( D'(-3, 2) \)

### Translation Calculation:
From \( A(1, -1) \) to \( A'(-3, 5) \):
- In the \( x \)-direction: \( 1 \to -3 \), which is a change of \( -4 \) units.
- In the \( y \)-direction: \( -1 \to 5 \), which is a change of \( +6 \) units.

Thus, the translation is \( (x, y) \to (x - 4, y + 6) \).

### Eric's Proposed Translation:
Eric suggests \( (x, y) \to (x + 6, y - 3) \). This is not correct based on the actual changes we observed.

### Correct Answer:
The correct translation should be \( (x, y) \to (x - 4, y + 6) \), which is not one of the options provided. However, we can conclude that **Eric is not correct**.

Would you like more details, or have any questions about this?

Here are 5 related questions to consider:
1. How can you verify a translation by comparing points?
2. What is the geometric significance of a translation in the coordinate plane?
3. Could Eric have made a mistake by interpreting the axes incorrectly?
4. How would the translation look if the parallelogram moved in the opposite direction?
5. What other transformations, besides translation, preserve the shape of a figure?

**Tip:** Always verify translations by checking both the \( x \)- and \( y \)-coordinate changes for at least one point!

Eric used the diagram below to translate ABCD parallelogram to a notation of (x,y)--> (x+6, y-3). Is he correct?

Explore whether Eric's translation notation (x,y)--> (x+6, y-3) for parallelogram ABCD is correct by analyzing the shift in coordinates. Detailed solution includes translation calculation and comparison of points A and A'. Suitable for middle school students studying coordinate geometry.

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