find the coordinate of a point with given distance from a given line.

Question

Given a line with coordinates $(a,b)$ and $(c,d)$ have a distance $\overline A$. Now, with a given distance $\overline B$ from the point $(a,b)$ , I want to get the coordinates $(x,y)$ where distance $\overline B$ ends.

Answer 1

You can use the Parametric form of line.

$$x= a+ R(\dfrac{c-a}{A}), y=a+R(\dfrac{d-b}{A})$$

Now if you put R=B and R=-B, you will get two points on the line which is your answer.