Question

write an equation in point slope form for the perpendicular bisector of the segment with the given endpoints M(1,5) N(7,-1)

Answer 1

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Answer 2

First I must apologize in advance for my not-so-good professional English, for I have learned Math in French!
Here is an approximative representation of the entire shebang:

Let U(MN)(a,b) be the direction vector of MN (the segment) : the coordinates of this vector are : a=7-1=6 and b=-1-5=-6 so we have U(MN)(6;-6).We notice that U(MN) is the normal vector of the right D; which gives us the equation of D:6x-6y+c=0. I order to find c, we need a point that belongs to D, which is the point of bisection of MN(the segment) and D.Let this point be I(r;s) : I is the midpoint of MN , so r=7+1/2=4 and s=5-1/2=2 and by virtue of that I(4;2). Let's return to D's equation in order to find c : 6x4-6x2+c=0 which means c+12=0 so c=-12 and from there we can conclude that D:6x-6y-12=0. And you happen to be in need for the equation in point slope form so :D:y=x-2.
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