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If point P is 4/7 of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

4:1
4:3
4:7
4:10

Respuesta :

lucic

Answer:

4:3

Step-by-step explanation:

Given that P divides segment MN into 4/7, let MN to be x units in length then

MP = 4/7 x =4x/7 --------(i)

But MN =MP+PN so;

x=4x/7 +PN

x- 4X/7 =PN

3x/7 =PN ----------(ii)

To get the ratio of MP:PN

MP: PN

4x/7:3x/7

MP/PN = 4x/7 / 3x/7

MP/PN =4/3

MP:PN = 4:3

JeanaShupp

Answer: 4:3

Step-by-step explanation:

Given : A point P is 4/7 of the distance from M to N.

∴ Let the distance between M to N be d.

[tex]\Rightarrow\ MP=\dfrac{4}{7}\times d=\dfrac{4d}{7}[/tex]

Also,  the point P partition the directed line segment from M to N .

Thus , MN = MP+PN

[tex]\Rightarrow\ d=\dfrac{4d}{7}+PN\\\\\Rightarrow\ PN= d-\dfrac{4d}{7}=\dfrac{7d-4d}{7}\\\\\Rightarrow\ PN=\dfrac{3}{7}d[/tex]

Now, the ration of MP to PN will be :-

[tex]\dfrac{MP}{PN}=\dfrac{\dfrac{4d}{7}}{\dfrac{3d}{7}}=\dfrac{4}{3}[/tex]

∴ Point P partitioned the line segment MN into 4:3.

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