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

therefore, tue coordinates is (-2.5, 1)