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If a point P lies on the line segment jo...

If a point `P` lies on the line segment joining points `A(-3, 4) and B(-2, -6)` such that `" "2AP=3BP`
then, find the co-ordinates of point P.

Text Solution

Verified by Experts

Given that,
`" "2AP=3BP`
` rArr" " (AP)/(BP)=(3)/(2)`
`rArr" "m:n=3:2`
`" "(x_(1), y_(2))=(-3, 4) and (x_(2),y_(2))=(-2, -6)`
Now, let the co-ordinates of point P are `(x, y)`
` therefore" "x=(3(-2)+2(-3 ))/(3+2)=(-12)/(5)`
`and " " y=(3(-6)+2(4))/( 3+2)=-2`
`therefore` Co-ordinates of point ` P =((-12)/(5),-2)`
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