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To solve the problem, we need to find the new coordinates of the triangle's vertices after the given translation. The translation rule is \( (x, y) \rightarrow (x + 2, y + 3) \), which means we add 2 to the x-coordinate and 3 to the y-coordinate for each vertex.

### Step 1: Identify the current coordinates of the vertices
Looking at the graph:
- The first vertex is approximately \( (-6, 2) \).
- The second vertex is approximately \( (-2, 4) \).
- The third vertex is approximately \( (-4, -2) \).

### Step 2: Apply the translation
Using the rule \( (x, y) \rightarrow (x + 2, y + 3) \):
1. For \( (-6, 2) \):
   \[
   (-6 + 2, 2 + 3) = (-4, 5)
   \]
2. For \( (-2, 4) \):
   \[
   (-2 + 2, 4 + 3) = (0, 7)
   \]
3. For \( (-4, -2) \):
   \[
   (-4 + 2, -2 + 3) = (-2, 1)
   \]

### Step 3: New Coordinates
The new coordinates of the vertices after the translation are:
- \( (-4, 5) \)
- \( (0, 7) \)
- \( (-2, 1) \)

Would you like further details or clarifications on this solution?

Here are 5 related questions to expand your understanding:
1. How would the translation \( (x, y) \rightarrow (x - 3, y + 1) \) affect the triangle's position?
2. What is the formula for translating a shape in the coordinate plane by any given translation vector?
3. How would you translate the triangle to the origin (0, 0)?
4. How does translation differ from other transformations like rotation or reflection?
5. What is the effect of translating a figure by \( (0, 0) \)?

**Tip:** Translations preserve the shape and size of figures, meaning the triangle after translation remains congruent to the original.

What are the coordinates of the vertices of the triangle under the translation (x, y) → (x + 2, y + 3)?

Learn how to find the new coordinates of a triangle's vertices after applying the translation (x, y) → (x + 2, y + 3). This example illustrates how translation affects the position of a shape in coordinate geometry. Suitable for students in Grades 6-8.

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