Question

find the ratio in which the line segment joining the points - 3, 10 and 6 - 8 is divided by minus 1,6​

Answer 1

Here x₁ = -3, y₁ = 10, x₂ = 6, y₂ = -8  

         [m(6) + n (-3)]/(m+n) , [m (-8) + n (10)]/(m+n) = (-1,6) 

        (6m - 3n)/(m+n), (-8m+10n)/(m+n) = (-1,6)

 equating the coefficients of x and y

    (6m-3n)/(m+n) = -1       (-8m+10n)/(m+n) = 6

       6m -  3n = -1 (m+n)

     6m - 3n = -1 (m+n)

      6m-3n=-m-n

      6m+m=-n+3n

       7m=2n

        m/n= 2/7

        m:n = 2:7

So the point (-1,6) is dividing the line segment in the ratio 2:7.

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Answer 2

EllØ :-

Answer

Let the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k : 1.Therefore, -1 = 6k-3/k+1

-k - 1 = 6k -3

7k = 2

k = 2/7

Therefore, the required ratio is 2:7.