One crucial fact about parallelograms we can take advantage of is that their diagonals bisect each other - they split one another in half, in other words. One thing we know about halves is that one half is always equal to the other, so looking at the halves of these diagonals, we can make two conclusions:
[tex] m+9.1=4k-3.5\\m=2.6k [/tex]
From these two equations, we have enough information to find k. Using the second equation, the substitution property of equality lets us replace the m in the first with 2.6k, giving us the equation
[tex] 2.6k+9.1=4k-3.5 [/tex]
by adding 3.5 and subtracting 2.6k from both sides, we get all of our k's on one side and all of our constants on the other:
[tex] 9.1 + 3.5 = 4k-2.6k\\12.6=1.4k [/tex]
Diving both sides by 1.4, we find that
[tex] k=12.6/1.4=9 [/tex]
The only option with k = 9 is C., so that's our answer.
