Find the equation of the perpendicular bisector of the straight line segment joining the points (3, 4) and (–1, 2).

Given: There is a perpendicular bisector of the straight line segment joining the points (3, 4) and (–1, 2).

We have to find the equation of the perpendicular bisector.

As it is perpendicular to the given line segment,the product of their slopes is equal to –1 and as it bisects the line segment,it implies it divides the line segment into 2 equal parts.

Thus,mid–point of the line segment joining the points (3, 4) and (–1, 2) is:

; where (x1,y1) and (x2,y2) are the end points of the line segment

=

=

=

= 1,3

Therefore the mid–point is (1,3).

The slope of the line segment joining the points (3, 4) and

(–1, 2) is:

⇒

⇒

Therefore the equation of the perpendicular bisector is

(y–y1) = m(x–x1)

Now substitute the value of the mid–point(1,3) and slope in the above equation.

⇒ 2(y–3) = (x–1)

⇒ 2y –6 = x–1

⇒ 2y–6–x + 1 = 0

⇒ –x + 2y–5 = 0

⇒ x–2y + 5 = 0 (multiply by –1 on both the sides of the equation)