Find the equation of the perpendicular bisector of the line segment obtained on joining the points (6, -3) and (0, 3).

Let points be A(6, -3) and B(0, 3) and D be the mid-point of AB.

Co-ordinates of D = $\Big(\dfrac{6 + 0}{2}, \dfrac{-3 + 3}{2}\Big) = \Big(\dfrac{6}{2}, \dfrac{0}{2}\Big)$ = (3, 0).

Slope of AB = $\dfrac{3 - (-3)}{0 - 6} = \dfrac{3 + 3}{-6} = \dfrac{6}{-6}$ = -1.

Let slope of perpendicular bisector be m.

Then

⇒ m × Slope of AB = -1

⇒ m × -1 = -1

⇒ m = 1.

Perpendicular bisector of AB will pass through mid-point of AB i.e. D.

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = 1(x - 3)

⇒ y = x - 3.

Hence, equation of the perpendicular bisector of the line segment obtained on joining the points (6, -3) and (0, 3) is y = x - 3.