Answer:
To find the coordinates of the vertex B' after the translation and dilation, follow these steps:
1. **Translation:** Move B left by 3 units and up by 2 units.
\[ B'(\text{{new }} x, \text{{new }} y) = (B_x - 3, B_y + 2) \]
2. **Dilation:** Dilate B' by a scale factor of 4 about the origin.
\[ B'(\text{{final }} x, \text{{final }} y) = (4 \cdot B'_x, 4 \cdot B'_y) \]
Apply these steps to the coordinates of B to find the new coordinates of B'.
If the coordinates of B are given as (x, y), the calculations would be as follows:
\[ B'(\text{{final }} x, \text{{final }} y) = (4 \cdot (B_x - 3), 4 \cdot (B_y + 2)) \]
Substitute the actual values for B_x and B_y to get the final coordinates of B'.
