Question

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?

Answer 1

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

Answer 2

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.

$\Rightarrow\ MP=\dfrac{4}{7}\times d=\dfrac{4d}{7}$

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

Thus , MN = MP+PN

$\Rightarrow\ d=\dfrac{4d}{7}+PN\\\\\Rightarrow\ PN= d-\dfrac{4d}{7}=\dfrac{7d-4d}{7}\\\\\Rightarrow\ PN=\dfrac{3}{7}d$

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

$\dfrac{MP}{PN}=\dfrac{\dfrac{4d}{7}}{\dfrac{3d}{7}}=\dfrac{4}{3}$

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