Bonus (Challenge) If a line segment has endpoints \( A(3 x+5,3 y) \) and \( B(x-1,-y) \) what are the coordinates of the midpoint of \( A B \) ? 1) \( (x+3,2 y) \) 2) \( (2 x+2, y) \) 3) \( (2 x+3, y) \) 4) \( (4 x+4,2 y) \)

To find the midpoint of a line segment with endpoints \( A(3x+5, 3y) \) and \( B(x-1, -y) \), we use the midpoint formula, which states that the coordinates of the midpoint \( M \) can be calculated as: \[ M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \] In this case, \( x_1 = 3x + 5 \), \( y_1 = 3y \), \( x_2 = x - 1 \), and \( y_2 = -y \). Calculating the midpoint: \[ M_x = \frac{(3x + 5) + (x - 1)}{2} = \frac{4x + 4}{2} = 2x + 2 \] \[ M_y = \frac{3y + (-y)}{2} = \frac{2y}{2} = y \] Thus, the coordinates of the midpoint \( M \) are \( (2x + 2, y) \). So, the answer is \( 2) (2 x + 2, y) \).