Answer: Point P partitioned the line segment MN into 4:3.
Step-by-step explanation:
Point P is [tex]\dfrac47[/tex]of the distance from M to N.
Let the distance between M to N =x.
[tex]MP=\dfrac47x[/tex]
Point P partition the directed line segment from M to N .
MN = MP+PN
[tex]\Rightarrow\ x=\dfrac47 x+PN\\\\\Rightarrow\ PN =x-\dfrac47 x\\\\\Rightarrow\ PN=\dfrac37 x[/tex]
Ratio of MP to PN = [tex]=\dfrac{\dfrac{4}{7}x}{\dfrac{3}{7}x}=\dfrac43[/tex]
∴ Point P partitioned the line segment MN into 4:3.
