Reduce distance between two points by %

Question

I have two points, say A = (2, 6) and B = (5, 3). I want to move point B up to 70% closer to point A. I calculate Euclidean distance between two points - it is 4.24. Then I calculate 70% from 4.24 and get 1.27, which will be a new distance between A and new point. How can I get to know what are the coordinates of that new point (point B that we moved)?

Answer 1

Put $t=0.7$ in

$$B + (A-B)t$$

to get the new point.