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Find the ratio in which point T(-1,6) di...

Find the ratio in which point `T(-1,6)` divides the line segment joining the points `P(-3,10) and Q(6,-8)`

Text Solution

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`P(-3,10),Q(6,-8)` and `T(-1,6)`.
Suppose the coordinates of point P are `(x_(1),y_(1))` the coordinates of point Q are `(x_(2),y_(2))` and the coordinates of point T are `(x,y)`.
Here `x_(1)=-3,y_(1)=10,x_(2)=6,y_(2)=-8,x=-1` and `y=6`.
By section formula,
`x=(mx_(2)+nx_(1))/(m+n)`
`:.-1=(m(6)+n(-3))/(m+n)`
`:.-1(m+n)=6m-3n`
`:.-m-n=6m-3n`
`:.6m+m=3n-n`
`:.7m=2n`
`:.m/n=2/7`
`:.m:n=2:7`
T divides line segment PQ in the ratio `2:7`.
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