# Reduce distance between two points by %

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)?

• move the x coordinate and y coordinate 70% closer separately. Then you should get the desired coordinate. If you draw a picture, everything should be clearer. – aNumosh Apr 14 '15 at 19:54
• The gross (but intuitively easy) way to do this is write down the equation of a circle centered at $A$ with radius $1.27$ and write down the equation of the line passing through both points. Solve the system of two equations. You'll get two intersections, so just decide which one is correct. Otherwise, take a weighted average of the points. – TravisJ Apr 14 '15 at 19:59
• $4.24\times \frac{70}{100}=2.968$ – Extremal Apr 14 '15 at 20:05

Put $t=0.7$ in
$$B + (A-B)t$$