Algebra

The equation of a perpendicular bisector of line segment AB can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept. The slope of the perpendicular bisector is the negative reciprocal of the slope of AB since the slope of a line perpendicular to AB is m2 = - 1/m1. The slope of line AB is m1 = (5-1)/(7-1) = 4/6 = 2/3. Therefore, the slope of the perpendicular bisector of AB is m2 = -3/2. The y-intercept b of the perpendicular bisector can be found by plugging the coordinates of A into the equation of the perpendicular bisector. Therefore, b = -3/2(1) + 1 = 1/2. Therefore, the equation of the perpendicular bisector of line AB is y = -3/2x + 1/2.