Question

What are the coordinates of the point on the directed line segment from (-3, -9) to (4, 5) that partitions the segment into a ratio of 5 to 2?

Answer 1

the coordinates the partitions point is (x,y), and given m =5 and n = 2, then

for x

`\begin{gathered} x=(m(x2)+n(x1))/(m+n) \\ x=(5(4)+2(-3))/(5+2) \\ x=(20-6)/(7) \\ x=(14)/(7) \\ x=2 \end{gathered}`

for y

`\begin{gathered} y=(m(y2)+n(y1))/(m+n) \\ y=(5(5)+2(-9))/(5+2) \\ y=(25-18)/(7) \\ y=(7)/(7) \\ y=1 \end{gathered}`

answer: the coordinates are (2,1)