Write down the line of reflection in each case: \( \begin{array}{ll}\text { (1) } A(4 ; 3) \rightarrow A^{\prime}(-4 ; 3) & \text { (2) B }\end{array} \)

To find the line of reflection for the point \( A(4, 3) \) reflected to \( A'(-4, 3) \), we can follow these steps: 1. **Identify the midpoint** of the segment connecting points \( A \) and \( A' \). The midpoint \( M \) can be calculated using the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where \( (x_1, y_1) = (4, 3) \) and \( (x_2, y_2) = (-4, 3) \). \[ M = \left( \frac{4 + (-4)}{2}, \frac{3 + 3}{2} \right) = \left( \frac{0}{2}, \frac{6}{2} \right) = (0, 3) \] 2. **Determine the slope of the line connecting \( A \) and \( A' \)**. The slope \( m \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 3}{-4 - 4} = \frac{0}{-8} = 0 \] This indicates that the line connecting \( A \) and \( A' \) is horizontal. 3. **Find the line of reflection**. Since the line connecting \( A \) and \( A' \) is horizontal, the line of reflection will be vertical and will pass through the midpoint \( M(0, 3) \). The equation of a vertical line through \( x = 0 \) is: \[ x = 0 \] This is the y-axis. Thus, the line of reflection for case (1) is: \[ \text{Line of reflection: } x = 0 \] For case (2), you mentioned "B" but did not provide any coordinates or context. If you provide the coordinates or details for point B and its reflection, I can help you find the line of reflection for that case as well.