Question

If point P is 4/7 of the distance from M to N, then point P partitions the directed line segment from M to N into a __?__ ratio. 4:1 4:3 4:7 4:11

Answer 1

Point P partitions the directed line segment from M to N into a 4 : 11 ratio.

Explanation:

Since, point P is 4/7 of the distance from M to N,

`\implies (MP)/(MN)=(4)/(7)`

Let MP = 4x and MN = 7x,

Where x is any number,

⇒ PN = MP + MN = 4x + 7x = 11x,

Thus, the ratio at which P divides the line segment from M to N is,

`(MP)/(PN)=(4x)/(11x)=(4)/(11)`

Hence, point P partitions the directed line segment from M to N into a 4 : 11 ratio.

Answer 2

Let

x-------> the distance MN

we know that

`MP=(4)/(7)x \\\\PN=(3)/(7)x`

Find the ratio
`MP:PN`

`ratio=(MP)/(PN) \\ \\ratio= ((4/7)x)/((3/7)x) \\ \\ratio= (4)/(3)`

therefore

the answer is

`4:3`