3. Which of the following are the coordinates of point A' , the image of point A after a translation of (x-2, y-1)?

Question

*
Captionless Image
A' (2, 2)
A' (-4, -3)
A' (1, 5)
A' (-2, 0)

Answer 1

To determine the coordinates of point \( A' \) after a translation, we need to apply the given translation rule to the coordinates of the original point \( A \). However, since the coordinates of point \( A \) are not provided in the question, I'll demonstrate the general process using the translation (x-2, y-1).

Let's denote the original coordinates of point \( A \) as \( (x, y) \). After the translation by (x-2, y-1), the new coordinates \( (x', y') \) of point \( A' \) can be found as follows:

\[
x' = x - 2
\]
\[
y' = y - 1
\]

Without the specific coordinates of \( A \), we can't definitively solve the problem, but we can use the provided answer choices to see which one fits the translation rule for possible original coordinates \( (x, y) \).

### Check the given choices:
1. **A' (2, 2)**
Let’s assume the original coordinates \( (x, y) \) result in \( A' (2, 2) \):
\[
2 = x - 2 \\
\rightarrow x = 4
\]
\[
2 = y - 1 \\
\rightarrow y = 3
\]
So, the original coordinates would be \( (4, 3) \).

2. **A' (-4, -3)**
Let’s assume the original coordinates \( (x, y) \) result in \( A' (-4, -3) \):
\[
-4 = x - 2 \\
\rightarrow x = -2
\]
\[
-3 = y - 1 \\
\rightarrow y = -2
\]
So, the original coordinates would be \( (-2, -2) \).

3. **A' (1, 5)**
Let’s assume the original coordinates \( (x, y) \) result in \( A' (1, 5) \):
\[
1 = x - 2 \\
\rightarrow x = 3
\]
\[
5 = y - 1 \\
\rightarrow y = 6
\]
So, the original coordinates would be \( (3, 6) \).

4. **A' (-2, 0)**
Let’s assume the original coordinates \( (x, y) \) result in \( A' (-2, 0) \):
\[
-2 = x - 2 \\
\rightarrow x = 0
\]
\[
0 = y - 1 \\
\rightarrow y = 1
\]
So, the original coordinates would be \( (0, 1) \).

Each of these results shows that it is possible to get the given choices from specific original coordinates. Without more context, any of these points could be the image results from their respective starting points.

However, if more context was available or a specific original point \( A \) was given, that would determine the correct image \( A' \).