Question

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

Answer 1

Let A = (6, −3) and B = (0, 3).

We know the perpendicular bisector of a line is perpendicular to the line and it bisects the line, that it, it passes through the mid-point of the line.

Co-ordinates of the mid-point of AB are

`((6 + 0)/2, (-3 + 3)/2)`

= `(6/2, 0)`

= (3, 0)

Thus, the required line passes through (3, 0).

Slope of AB = `(3 + 3)/(0 - 6) = 6/(-6) = -1`

∴  Slope of the required line = `(-1)/("slope of AB") = 1`

Thus, the equation of the required line is given by:

y − y₁ = m(x − x₁)

y − 0 = 1(x − 3)

y = x – 3