https://file.aiquickdraw.com/mathbot/file/1727206682358tkxmdr8c.jpg

The problem asks for the coordinates of the vertices of the figure after a translation of **1 unit left** and **2 units up**.

### Step-by-Step Solution:

1. **Original Coordinates**: 
   - \( G( -3, -4 ) \)
   - \( H( -4, -1 ) \)
   - \( I( -1, 2 ) \)
   - \( J( -1, -3 ) \)

2. **Translation**:
   - Move **1 unit left**: This decreases the \( x \)-coordinate by 1 for each point.
   - Move **2 units up**: This increases the \( y \)-coordinate by 2 for each point.

### Translated Coordinates:

- **For \( G \)**:
  - Original: \( G( -3, -4 ) \)
  - New: \( G'( -3 - 1, -4 + 2 ) = G'( -4, -2 ) \)

- **For \( H \)**:
  - Original: \( H( -4, -1 ) \)
  - New: \( H'( -4 - 1, -1 + 2 ) = H'( -5, 1 ) \)

- **For \( I \)**:
  - Original: \( I( -1, 2 ) \)
  - New: \( I'( -1 - 1, 2 + 2 ) = I'( -2, 4 ) \)

- **For \( J \)**:
  - Original: \( J( -1, -3 ) \)
  - New: \( J'( -1 - 1, -3 + 2 ) = J'( -2, -1 ) \)

### Final Answer:
The translated coordinates are:
- \( G'( -4, -2 ) \)
- \( H'( -5, 1 ) \)
- \( I'( -2, 4 ) \)
- \( J'( -2, -1 ) \)

### Correct Choice:
- **Option A**: \( G'( -4, -2 ), H'( -5, 1 ), I'( -2, 4 ), J'( -2, -1 ) \).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What are the effects of different types of transformations like reflections or rotations?
2. How would the figure change with a translation 2 units right and 3 units down?
3. What are the rules for translating coordinates on a Cartesian plane?
4. How does the distance between points change after a translation?
5. What is the general formula for translating a point by \( (a, b) \)?

**Tip**: When translating, always adjust the \( x \)-coordinate for horizontal movement and the \( y \)-coordinate for vertical movement.

Find the coordinates of the vertices of each figure after the given translation: 1 unit left and 2 units up.

Find the new coordinates of vertices after translating a shape 1 unit left and 2 units up. This problem involves basic geometric transformations on a coordinate plane, suitable for students in Grades 6-8.

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