Write the equation of the perpendicular bisector of rs. point r is located at (–1, 3), and point s is located at (3, 1).

We have that
Point R is located at (–1, 3), and point S is located at (3, 1)

we know that
the perpendicular bisector of RS go through the midpoint of RS

step 1

find the midpoint RS

midpoint M (Mx,My)
Mx=(x1+x2)/2
My=(y1+y2)/2

Mx=(-1+3)/2------> Mx=1
My=(3+1)/2-------> My=2

the midpoint M is (1,2)

step 2
find the slope RS
m=(y2-y1)/(x2-x1)-------> m=(1-3)/(3+1)-----> m=-2/4-----> m=-1/2

we know that two lines are perpendicular if the slopes
m1*m2=-1

step 3
find the slope of the perpendicular bisector of RS
m2=-1/m1------> m2=2

step 4
 with m=2 and the midpoint M (1,2) find the equation of a line

y-y1=m*(x-x1)------> y-2=2*(x-1)----> y=2x-2+2-----> y=2x

the answer is
y=2x

see the attached figure

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