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.

Step-by-step explanation:

Given: Point P is $\dfrac{4}{7}$ 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

$\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}$

As per given,

$\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}$

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