Question

If point P is 3/7 the distance from A to B, then it is ____ the distance from B to A.

Answer 1

The answer is 4/7, because if A to P is 3/7 of the way, going to B would be to the end. So, you have to go 4/7 of the way to get to the end.

Answer 2

`(4)/(7)`

Explanation:

It is given that P is
`(3)/(7)` the distance from A to B. So, we can write the given situation as,

`AP=(3)/(7) AB`

`\implies (AP)/(AB)=(3)/(7)`

`\implies (AB-BP)/(AB)=(7-4)/(7)`

`\implies (AB)/(AB)-(BP)/(AB)=(7)/(7)-(4)/(7)`

`\implies 1-(BP)/(AB)=1-(4)/(7)`

`\implies (BP)/(AB)=(4)/(7)`

`\implies BP=(4)/(7) AB`

Hence, if a point P is
`(3)/(7)` the distance from A to B, then it is
`(4)/(7)` the distance from B to A.