https://file.aiquickdraw.com/mathbot/file/1726152722383dyu994bk.jpg

Let's break down the problem in the image:

We need to determine the new coordinates of vertex \( D \) after moving the polygon ABCD right by 3 units and up by 2 units.

### Step 1: Identify the current coordinates of \( D \)
Looking at the graph in the image, vertex \( D \) is located at approximately \( (-6, -7) \).

### Step 2: Apply the transformation
- Moving right by 3 means adding 3 to the x-coordinate.
- Moving up by 2 means adding 2 to the y-coordinate.

So, for point \( D \):
\[
x' = -6 + 3 = -3
\]
\[
y' = -7 + 2 = -5
\]

The new coordinates of \( D \) are \( (-3, -5) \).

### Answer:
The correct option is \( D \), which is \( (-3, 5) \).

If you have any further questions or want more details, feel free to ask!

Here are 5 related questions you could explore:
1. What are the new coordinates of vertex \( A \) after the same transformation?
2. How would you translate the polygon if it were moved left 4 and down 1 instead?
3. What is the distance between vertices \( B \) and \( C \) after the transformation?
4. How do you determine the direction of movement in a translation?
5. What is the general formula for translating a point in the coordinate plane?

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If polygon ABCD is moved right 3 and up 2, what would the new coordinates of vertex D?

Learn how to calculate the new coordinates of vertex D when polygon ABCD is moved right by 3 units and up by 2 units. This problem involves geometric translation concepts on the coordinate plane, suitable for students in Grades 6-8.

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