Answer:
Step-by-step explanation:
a perpendicular bisector, bisects a line segment at
right angles
to obtain the equation we require slope and a point on it
find the midpoint and slope of the given points
midpoint
=
[
1
2
(
1
+
5
)
,
1
2
(
4
−
2
)
]
midpoint
=
(
3
,
1
)
←
point on bisector
calculate the slope m using the
gradient formula
∙
x
m
=
y
2
−
y
1
x
2
−
x
1
let
(
x
1
,
y
1
)
=
(
1
,
4
)
and
(
x
2
,
y
2
)
=
(
5
,
−
2
)
⇒
m
=
−
2
−
4
5
−
1
=
−
6
4
=
−
3
2
given a line with slope m then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
−
3
2
=
2
3
←
slope of bisector
using
m
=
2
3
and
(
x
1
,
y
1
)
=
(
3
,
1
)
then
y
−
1
=
2
3
(
x
−
3
)
←
in point-slope form
⇒
y
−
1
=
2
3
x
−
2
⇒
y
=
2
3
x
−
1
←
in slope-intercept form
Step-by-step explanation: