https://file.aiquickdraw.com/mathbot/file/1730203044839e0ihlae9.jpg

To solve this, we need to find the coordinates of vertex \( S \) after performing the given transformations. The transformations are:

1. **Reflection across \( y = 0 \)** (the x-axis).
2. **Translation 1 unit left and 2 units up**.

### Step-by-Step Solution:

1. **Identify the Initial Coordinates of \( S \)**:
   From the grid, \( S \) is located at \( (-3, -3) \).

2. **Reflection across \( y = 0 \)**:
   Reflecting \( S(-3, -3) \) across the x-axis will change the \( y \)-coordinate from \(-3\) to \(3\), resulting in the point:
   \[
   S' = (-3, 3)
   \]

3. **Translation (1 unit left and 2 units up)**:
   Moving \( S'(-3, 3) \) 1 unit to the left changes the \( x \)-coordinate from \(-3\) to \(-4\), and moving 2 units up changes the \( y \)-coordinate from \(3\) to \(5\). This results in:
   \[
   S'' = (-4, 5)
   \]

### Final Answer:
The coordinates of \( S \) after the sequence of transformations are:
\[
S = (-4, 5)
\]

Would you like more details on any of these steps, or have any questions?

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Here are some related questions to further explore this topic:

1. How does reflecting a point across the x-axis affect its coordinates?
2. How would a reflection across the y-axis change the coordinates of a point?
3. What would happen if the translation was 1 unit right and 2 units down instead?
4. How can we generalize the effect of reflections and translations on coordinates?
5. How would the transformations change if the reflection was across the line \( y = x \) instead?

**Tip:** When reflecting a point, only the coordinate perpendicular to the axis of reflection changes its sign.

Find the coordinates of point S after reflecting across y = 0 and translating 1 unit left and 2 units up.

Learn how to find the coordinates of a point after performing a reflection across the x-axis and a translation of 1 unit left and 2 units up. This problem explores key concepts in transformations and coordinate geometry, suitable for students in Grades 8-10.

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