Question 975942
This is correct.
The distance between the two points is the square root of the difference of the x s ^2 plus the square root of the difference of the ys ^2.  The distance is square root of (40)= which is 2 square root of 10.  Half the distance is the square root of 10.  square root of 40=square root of (4*10).

The equation of the line through the points has slope -2/6  or -1/3
y-y1=(-1/3)((x-x1)

y-3= (-1/3) (x-2)

y= -(1/3)x +(2/3)+3  =  -(1/3)x+11/3
perpendicular line has slope 3 (negative reciprocal)
goes through midpoint which is half the distance between the two points (5,2)

Its equation is y-2=3(x-5)

y=3x-13

{{{graph(300,200,-20,20,-20,20,(-x/3)+(11/3), 3x-13)}}}