how to find coordinate of a point on the triangle chord?

Question

I have a Right triangle with points ( a=(0,-2), b=(-5,-2), c=(-5,5) ). its chord length is d=8.6. I need to find coordinates of a point on chord (for example p=d/4.3=2) as a tuple of (x,y). is there a simple formula to solve this?

Answer 1

Using trig the equation of the hypotenuse is $y=(5-x)\tan \frac75-2.$ I leave it to you to show why this is right.