Question

plz find answer
quick it's urgent​

Answer 1

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Find the ratio in which the line segment joining the points (-3,10)and (6,-8) is divided by (-1,6)

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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

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.