Find the equation of the line perpendicular to and containing the midpoint of the segment joining (7,-20) and (3,10)

Find the equation of the line perpendicular to and containing the midpoint of the segment joining (7,-20) and (3,10)

The midpoint  =  [ (7 + 3)/2, (-20 + 10)/2 ]  =  [ 10/2, -10/2] =  [5, -5]

The slope of the line joining the two points is given by :

[10 - -20] / [ 3 - 7 ] =  [30/-4]  = [-15/2]

So....a line perpendicular to the one joining the two given points wil have a slope = 2/15.......and the equation is :

y - -5  =  (2/15)(x - 5)   simplify

y + 5   = (2/15)x - 2/3

y = (2/15)x - 17/3

Here's the graph : https://www.desmos.com/calculator/nuwyd9uvqe