Segment division with given ratio

Question

Find the coordinates of point $P$ that divides the segment $AB$ in a ratio of $1:3$ , given that A=$(2,1)$ , B=$(6,9)$ ?

Answer 1

the straight line through $A,B$ has the equation $$y=2x-3$$ and additionally we have $$\frac{\sqrt{(x-2)^2+(y-1)^2}}{\sqrt{(6-x)^2+(9-y)^2}}=\frac{1}{3}$$ Can you get it from here?