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?

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?

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

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Alaia 1 week 2021-09-09T10:54:23+00:00 2 Answers 0

Answers ( )

    0
    2021-09-09T10:55:32+00:00

    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.

    0
    2021-09-09T10:56:03+00:00

    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

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