Question

If A(2, 2) and B(14, 10) find the point that will divide AB into a ratio of 3:1 starting from point A.

Answer 1

Point
`(11,8)` divides
`AB` into a ratio of
`3:1` .

Explanation:

Given: Points are
`A(2,2)\,,\,B(14,10)`

To find: point that will divide
`AB` into a ratio of
`3:1` starting from point
`A`.

Solution:

If the point
`(x,y)` divides the line joining points
`A(u,v)` and
`B(p,q)` in ratio
`m:n` then

`(x,y)=((mp+nu)/(m+n),(mq+nv)/(m+n) )`

Put
`(u,v)=(2,2)\,,\,(p,q)=(14,10)\,,\,m:n=3:1`

Therefore,

`(x,y)=((3(14)+1(2))/(3+1) ,(3(10)+1(2))/(3+1) )=((42+2)/(4),(30+2)/(4))=((44)/(4),(32)/(4))=(11,8)`

Therefore,

point
`(11,8)` divides
`AB` into a ratio of
`3:1` .