3. Which image is the translation of Triangle ABC given by the translation rule (x,y)→ (x-2, y+3)

Answer 1

To determine which image is the translation of Triangle ABC according to the translation rule \((x, y) \to (x - 2, y + 3)\), we follow these steps:

1. **Identify the vertices of Triangle ABC before the translation**: Let’s denote the vertices of Triangle ABC as \(A(x_1, y_1)\), \(B(x_2, y_2)\), and \(C(x_3, y_3)\).

2. **Apply the translation rule to each vertex**:
- Vertex A: \((x_1, y_1)\) translates to \((x_1 - 2, y_1 + 3)\).
- Vertex B: \((x_2, y_2)\) translates to \((x_2 - 2, y_2 + 3)\).
- Vertex C: \((x_3, y_3)\) translates to \((x_3 - 2, y_3 + 3)\).

3. **Plot the new vertices to determine the image of the translated triangle**: The new vertices after the translation will be:
- New Vertex A: \(A'(x_1 - 2, y_1 + 3)\),
- New Vertex B: \(B'(x_2 - 2, y_2 + 3)\),
- New Vertex C: \(C'(x_3 - 2, y_3 + 3)\).

By plotting these new vertices, we can identify the new triangle A'B'C', which is the image of Triangle ABC after the given translation.

Without a specific diagram or coordinates, it is necessary to apply these rules to determine the new position of each vertex. If you have a visual reference like a graph or plotted points, you would locate points \(A'B'C'\) based on the translated coordinates, ensuring the vertices are shifted 2 units to the left and 3 units up from their original positions.