# The points (1,6) and (12,9) are the two opposite vertices of a parallelogram. the other two vertices lie on the line 3y=11 x+k. then k is

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The Brainliest Answer!

Let (12,9) be pt-B

So, mid-point of line AB=((12+1)/2,(9+6)/2)

=(13/2,15,2)

As in a parallelogram,the diagonals bisect each-other,(13/2,15/2)lies on line-3y=11x+k

so,BTP,

3x(15/2)=11x(13/2)+k

So,k=45/2-143/2

so,k=-98/2=-49

The midpoint of the diagonal =

This midpoint lies on the equation 3y = 11x + k

3(15/2) = 11(13/2) + k

45/2 = 143/2 + k

k = 45/2 - 143/2

k = -98/2 = -49