Find the equation of the perpendicular bisector of the line segment joining the points A(2, 3) and B(6, -5).

Explanation

The slope of AB is given by
`m = (-5-3)/(6-2) = -2`
Therefore, the slope of the line perpendicular to AB is
` -(1)/(m) = (1)/(2)`
Let P be the midpoint of AB. Then, the coordinates of P are
`((2+6)/(2) , (3-5)/(2))`, i.e., (4,-1)
Thus, the required line passes through P(4,-1) and has slope 1/2.
So, its equation is
`y+1 = (1)/(2)(x-4) " " [("Using " y-y_(1) = m(x_(1)-x_(1))]`
or x-2y-6 = 0