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Given A(4,-3) ,B (8,5) . Find the coordi...

Given A(4,-3) ,B (8,5) . Find the coordinates of the point that
divides segment AB in the ratio ` 3: 1`

Text Solution

Verified by Experts

`A(4,-3)` and `B(8,5)`
Let `P(x,y)` divide segment AB in the ratiio `3:1`.
`:.m:n=3:1`
Let `A(x_(1),y_(1))` and `B(x_(2),y_(2))`
Here `x_(1)=4,y_(1)=-3,x_(2)=8` and `y_(2)=5`
By section formula,
`x=(mx_(2)+nx_(1))/(m+n), y=(my_(2)+ny_(1))/(m+n)`
`:.x=(3(8)+1(4))/(3+1),:.y=(3(5)+1(-3))/(3+1)`
`:.x=(24+4)/4,:.y=(15-3)/4`
`:.x=28/4, :.y=12/4`
`:.x=7, :.y=3`
Point (7,3) divides segment AB in the ratio `3:1`.
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