Question

You have a line AB where A is (0,3) and Bis (3,9) find a point P that partitions the line 1:2.

Answer 1

If a line with coordinates (x1, y1) and (x2, y2) is partitioned at point P in a ratio a:b, point P is located at:

$(x_1+\frac{a}{a+b}(x_2-x_1),y_1+\frac{a}{a+b}(y_2-y_1))$

In this case, the points are A(0,3) and B(3,9), and the ratio is 1:2, then P is located at:

$\begin{gathered} (0+\frac{1}{1+2}(3-0),3+\frac{1}{1+2}(9-3)) \\ (0+\frac{1}{3}\cdot3,3+\frac{1}{3}\cdot6) \\ (1,5) \end{gathered}$