https://file.aiquickdraw.com/mathbot/file/1726767738205to82ybbc.jpg

Let's solve the problem from the image. The task is to translate quadrilateral \(ABCD\) by 2 units to the right and 4 units up, and find the new coordinates of \(A'B'C'D'\).

### Current coordinates:
- \(A(5, 2)\)
- \(B(7, 4)\)
- \(C(9, 2)\)
- \(D(7, 0)\)

### Translation:
- 2 units to the right means adding 2 to the \(x\)-coordinate.
- 4 units up means adding 4 to the \(y\)-coordinate.

### Applying the translation:
1. **For point A**:
   \[
   A(5, 2) \rightarrow A'(5 + 2, 2 + 4) = A'(7, 6)
   \]
2. **For point B**:
   \[
   B(7, 4) \rightarrow B'(7 + 2, 4 + 4) = B'(9, 8)
   \]
3. **For point C**:
   \[
   C(9, 2) \rightarrow C'(9 + 2, 2 + 4) = C'(11, 6)
   \]
4. **For point D**:
   \[
   D(7, 0) \rightarrow D'(7 + 2, 0 + 4) = D'(9, 4)
   \]

### New coordinates:
- \(A'(7, 6)\)
- \(B'(9, 8)\)
- \(C'(11, 6)\)
- \(D'(9, 4)\)

### Checking the options:
The coordinates \(A'(7, 6)\), \(B'(9, 8)\), \(C'(11, 6)\), and \(D'(9, 4)\) are not directly provided in the multiple-choice answers, which suggests there might be an issue in interpretation or rounding. However, based on the translation logic, the coordinates match the transformation correctly.

Let me know if you'd like to explore further. 

Here are 5 questions to deepen your understanding:
1. How do you apply translations to shapes on a coordinate plane?
2. Can a figure's orientation change with a translation?
3. What is the difference between translation and rotation?
4. How would the figure change if you translated it down and left instead?
5. How would this problem change if the translation was by fractions?

**Tip:** In translations, always remember that both the direction and the magnitude affect only the position, not the shape or size of the figure.

Translate quadrilateral ABCD by 2 units to the right and 4 units up. Which of the following are the coordinates of new quadrilateral A'B'C'D'?

Learn how to translate quadrilateral ABCD by 2 units to the right and 4 units up. Find the new coordinates of A', B', C', and D' after applying the translation. This problem focuses on key geometry concepts related to translation on the coordinate plane, ideal for Grades 7-9.

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