I have tried to find posts that are related to the question but they end up with the terms like ‘find a distance’. What I want is not to find the distance: I already have the distance, I want something else.
Assume $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line $y=ax+b$ and the euclidean distance between the points is defined as $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$.
Known:
point $(x_1,y_1)$
line $y=ax+b$
distance $d$
Unknown:
point(s?) $(x_2,y_2)$
I want to know whether I am on the right path. Should I solve for the line and the distance formula to find $x_2,y_2$? Is this the right way? Is there any faster way of doing this?