# Thread: Geometry Finding a coordinate

1. ## Geometry Finding a coordinate

Given A(2,12) and B(5,0) find the coordinates of P such that P seperates AB in two two parts with a ratio 2 to 1? I do not know how to set this problem up please help me. Thank you

2. Hello, IDontunderstand!

Given $\displaystyle A(2,12)$ and $\displaystyle B(5,0)$, find the coordinates of point $\displaystyle P$
that seperates $\displaystyle AB$ into two parts with ratio 2:1.

If P is $\displaystyle \tfrac{2}{3}$ of the way from $\displaystyle A$ to $\displaystyle B$, then:
. . the $\displaystyle x$-coordinate is $\displaystyle \tfrac{2}{3}$ of the way from 2 and 5 (the two $\displaystyle x$-coordinates)
. . the $\displaystyle y$-coordinate is $\displaystyle \tfrac{2}{3}$ of the way from 12 and 0 (the two $\displaystyle y$-coordindates).

. . . . $\displaystyle \begin{array}{ccccc}x &=& 2 + \tfrac{2}{3}(5-2) &=& 4 \\ \\[-4mm] y &=& 12 + \tfrac{2}{3}(0-12) &=& 4 \end{array}$

Therefore: .$\displaystyle P(4,4)$