3. A \( (-4,2), \mathrm{B}(0,1) \) and \( \mathrm{C}(-2,-3) \) are the vertices of \( \Delta \mathrm{ABC} \). If \( A^{\prime}(-1,6) \) be the image under the translation of vertex \( A \). Find the images \( B^{\prime} \) and \( C^{\prime} \) of B and C under the same translation.

To find the images \( B' \) and \( C' \) under the same translation that transformed vertex \( A \) into \( A' \), we first need to determine the translation vector that was used. The translation vector can be derived by subtracting the coordinates of \( A \) from those of \( A' \): \[ \text{Translation Vector} = A' - A = (-1, 6) - (-4, 2) = (3, 4). \] Now, we apply this translation vector to points \( B \) and \( C \). For point \( B(0, 1) \): \[ B' = B + \text{Translation Vector} = (0 + 3, 1 + 4) = (3, 5). \] For point \( C(-2, -3) \): \[ C' = C + \text{Translation Vector} = (-2 + 3, -3 + 4) = (1, 1). \] Thus, the images are: \[ B' = (3, 5) \quad \text{and} \quad C' = (1, 1). \]