https://file.aiquickdraw.com/mathbot/file/17257340746151zkxowkm.jpg

The image shows a triangle with points \( B \), \( G \), and \( T \), and a transformation instruction: **"translation: 5 units right and 1 unit up."** The task is to find the new coordinates of points \( B \), \( G \), and \( T \) after applying the translation.

### Steps for translation:
- Translation moves every point by a certain amount. In this case, each point is moved:
  - **5 units to the right** (add 5 to the x-coordinate).
  - **1 unit up** (add 1 to the y-coordinate).

### Identifying the coordinates:
1. From the graph, the coordinates of the original points appear to be approximately:
   - \( B(x_1, y_1) = (-6, -4) \)
   - \( G(x_2, y_2) = (-6, -2) \)
   - \( T(x_3, y_3) = (-2, -2) \)

### Applying the translation:
- **B'**: \((-6 + 5, -4 + 1) = (-1, -3)\)
- **G'**: \((-6 + 5, -2 + 1) = (-1, -1)\)
- **T'**: \((-2 + 5, -2 + 1) = (3, -1)\)

### New coordinates after the translation:
- \( B'( -1, -3 ) \)
- \( G'( -1, -1 ) \)
- \( T'( 3, -1 ) \)

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What are other types of transformations besides translation?
2. How can we mathematically represent a translation?
3. What is the difference between translation and reflection?
4. How do translations affect the shape and size of a figure?
5. How can translations be combined with other transformations?

**Tip:** Always check the direction and magnitude of the translation carefully, as positive and negative directions can change the outcome.

Translate the points of the triangle by 5 units to the right and 1 unit up.

Learn how to translate a triangle on a coordinate plane by 5 units to the right and 1 unit up. This problem demonstrates the application of coordinate translation, where each point is moved according to the transformation formula. Suitable for students in Grades 6-8.

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