The coordinates of the point which partitions a directed line segment AB at the ratio a:b from A(x1, y1) to B(x2, y2) is computed as follows:
[tex](x,y)=(x_1+\frac{a}{a+b}(x_2-x_1),y_1+\frac{a}{a+b}(y_2-y_1_{}))[/tex]In this case, the segment goes from R(-2, 4) to S(18, -6), and the partition ratio is 3:7. Substituting into the above formula, we get:
[tex]\begin{gathered} (x,y)=(-2+\frac{3}{3+7}(18-(-2)),4+\frac{3}{3+7}(-6-4)) \\ (x,y)=(-2+\frac{3}{10}\cdot20,4+\frac{3}{10}(-10)) \\ (x,y)=(4,1) \end{gathered}[/tex]