The equation of the line between the points (6, 3) and (3, 4) is y – 3 = (x – 6)[(4 – 3)/(3 – 6)]

=> y – 3 = (x – 6)*( -1/3)

The slope of the line is (-1/3). The equation of the line perpendicular of this is 3. The midpoint of the given points is [( 6 + 3)/2 , (4 + 3)/2] = ( 9/2 , 7/2 )

The equation of the perpendicular bisector is y – 7/2 = 3( x – 9/2)

=> 2y – 7 = 6x – 27

=> 6x – 2y – 20 = 0

=> 3x – y – 10 = 0

The required equation of the perpendicular bisector is  3x – y – 10 = 0