Question

If point P is 4/7 of the distnace frm M to N, what ratio does the point P partiion the directed line segment from M to N

Answer 1

Answer: 4:3.

Explanation:

Given: Point P is
`(4)/(7)` of the distance from M to N.

To find: The ratio in which the point P partition the directed line segment from M to N.

If Point P is between points M and N, then the ratio can be written as

`(MP)/(MN)=(MP)/(MP+PN)`

As per given,

`(MP)/(MP+PN)=(4)/(7)\\\\\Rightarrow\ (MP+PN)/(MP)=(7)/(4)\\\\\Rightarrow\ (MP)/(MP)+(PN)/(MP)=(7)/(4)\\\\\Rightarrow\ -1+(PN)/(MP)=(7)/(4)\\\\\Rightarrow\ (PN)/(MP)=(7)/(4)-1=(7-4)/(4)=(3)/(4)\\\\\Rightarrow\ (PN)/(MP)=(3)/(4)\ \ \or\ (MP)/(PN)=(4)/(3)`

Hence, P partition the directed line segment from M to N in 4:3.