Question

What are the coordinates of the point on the directed line segment from (-5,–9) to(-1,7) that partitions the segment into a ratio of 5 to 3?

Answer 1

We have the following:

$\begin{gathered} x_1+r\cdot(x_2-x_1) \\ y_1+r\cdot(y_2-y_1) \\ r=\frac{5}{5+3}=\frac{5}{8} \\ x_1=-5;x_2=-1 \\ y_1=-9;y_2=7 \\ -5+\frac{5}{8}\cdot(-1-(-5))=-5+\frac{5}{8}(4)=-2.5 \\ -9+\frac{5}{8}\cdot(7-(-9))=-9+\frac{5}{8}(16)=1 \end{gathered}$

therefore, tue coordinates is (-2.5, 1)