I was solving a problem that required me to find some points in the plane perpendicular to a segment that I already had. Since I am applying the fact that the dot product of the vector I already have and the new vector I am trying to discover is zero (assuming that they are perpendicular), and considering that I also know the length of this new vector I am trying to discover, I wrote a system of equations:
$ 550 x + 350 y = 0 \\ 50 = \sqrt{ (x - 150)^2 + (y - 50)^2 } $
Before I started solving by myself, I checked the solution in Wolfram Alpha, and yes. The results are exactly the points I need to create my new segment, perpendicular to the one I had.
But when solving "by hand", I could do the first equation, but when trying to solve the second one, I arrived to a moment when I get as a result a square root of a negative number, and I have no idea about how to continue from there.
I am solving the lower equation using:
$ (a-b)^2 = a^2-2ab+b^2 $
Is this the right method or I have to do something else?
I am not very good at this, so I am trying to read as much as I can to understand how this works, but for the moment I am having trouble. Any comment regarding this problem will be much appreciated.
Thanks!