Question

If point P is 9/11 of the distance from M to N, then point P partitions the directed line segment from M to N into a ____ ratio.

Answer 1

If point P is 9/11 of the distance from M to N, then point P partitions the directed line segment from M to N into a 9:2 ratio

Answer 2

The ratio will be 9 : 2

Explanation:

Suppose, the distance from
`M` to
`N` is
`x`

As point P is
`(9)/(11)` of the distance from
`M` to
`N`, so the length of the line segment
`\overline{MP}` will be:
`(9)/(11)x`

Now,
`\overline{PN}=\overline{MN}-\overline{MP} = x-(9)/(11)x = (2)/(11)x`

Thus,
`\overline{MP}: \overline{PN}= (9)/(11)x:(2)/(11)x =9:2`

So, the point
`P` partitions the directed line segment from
`M` to
`N` into 9 : 2 ratio.