calculate a perpendicular offset from a diagonal line

I am writing a music display program and need to draw a 'slur' between two notes. A slur is a curved line linking two notes - just to be clear.

I know the note positions and calculate where the start and end points of the curve should be - Start point A and End point B.

I now need to obtain the offset C, given the distance required, for use within a quadratic curve. This is where my, very, limited knowledge and understanding of maths formulae comes in.

I have indeed looked here in SO for my answer, but the solutions proposed either do not work or I am too limited to code them correctly.

Can someone help me with the calculation, in a NON mathematical form ?