What is the equation of the perpendicular bisector of the line between (6, 3) and (3, 4)?

Since the line is the bisectrix of the segment whose
endpoints are (6, 3) and (3, 4), the midpoint of the segment is on this
line.

We'll calculate the
midpoint:

x mid = (6+3)/2

x
mid = 9/2

y mid = (3+4)/2

y
mid = 7/2

Since the bisectrix is perpendicular on the
segment, the product of the slopes of the perpendicular lines is
-1.

First, we'll write the equation of the
segment:

(6-3)/(x-3) =
(3-4)/(y-4)

3/(x-3) =
-1/(y-4)

-x + 3 = 3y -
12

We'll put the equation in the slope intercept
form:

3y = -x + 15

y = -x/3 +
5

The slope of the segment line is m1 =
-1/3

m2*m1 = -1

m2 =
-1/m1

m2 = 3

The equation of
the perpendicular line is:

y - ymid = m2(x -
xmid)

y - 7/2 = 3(x - 9/2)

(2y
- 7)/2 = (6x - 27)/2

We'll simplify and we'll
get:

2y - 7 = 6x - 27

The
equation of the perpendicular bisectrix line is 6x - 2y - 20 =
0.

We'll simplify and we'll
get:

3x - y - 10 =
0