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) \( (4 x+4,2 y) \)

1. The midpoint \((M)\) of a segment with endpoints \((x_1,y_1)\) and \((x_2,y_2)\) is given by: \[ M\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) \] 2. For endpoint \( A \) with coordinates \((3x+5,\, 3y)\) and endpoint \( B \) with coordinates \((x-1,\,-y)\): - The \(x\)-coordinate of the midpoint: \[ \frac{(3x+5) + (x-1)}{2} = \frac{3x+5+x-1}{2} = \frac{4x+4}{2} = 2x+2 \] - The \(y\)-coordinate of the midpoint: \[ \frac{3y+(-y)}{2} = \frac{3y-y}{2} = \frac{2y}{2} = y \] 3. Thus, the coordinates of the midpoint are: \[ (2x+2,\, y) \] The correct choice is 2) \( (2x+2,\, y) \).