How do I find point B of line AB with only point A, distance, and slope?

Question

Good morning. There is a line AB and A is at point (x, y). x and y are known. So is the slope (m) and distance (time).

Is there a formula to calculate the x and y value separately of point B?

Answer 1

I believe time is straightforward and B is later then A.

Then $$x_B=x_A+ distance \cdot \frac{1}{\sqrt{1+slope^2}}$$ $$y_B=y_A + distance \cdot \frac{slope}{\sqrt{1+slope^2}}$$

Answer 2

I'm not sure if I entirely understand what you're asking. But I think you get a right triangle where you know the ratio of the leg lengths (via the slope) and the length of the hypotenuse ("distance"). You should be able to find any remaining parts based on this information and the Pythagorean Theorem. On the other hand, if "distance" refers to change in just $x$, then you know a leg and the ratio of the legs, and again you can proceed from there.

Once you have the values for the two legs, you should be able to find point $B$.