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    Ok so your first step is to find the coordinates of C, given you know A and M. Then you can use the ratios of lengths to find the coordinates of N. Finally, work out the distance between N and B.
    Hope this helps if not, I can be more specific
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    more specific please
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    (Original post by Official-21)
    more specific please
    Alright so first off, I was slightly wrong. You need the coords of C and B. You also don't use the ratios on the lengths as such.
    First find C. You know A and M and since the M is the midpoint, AM = MC. AM = (5,-2.5) so add this to M gives C = (8,2) You can check this as it shares the y coord with D. Then to get B, you use the fact that AB = DC giving B = (11,7).
    Then you use the ratios to find the location of N. So we know AM is (5,-2.5) So divide by 5 and times by 3 to give MN as (3,-1.5). Add this to M giving N as (6,3).
    Now you know N and B so use pythagoras to find the length between them I got the final answer as square root of 41 since it wants the exact length.

    Hope this was useful
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    how did you get AM= 5,-2.5
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    AM is M minus A so (3 - -2, 4.5 - 7) so (5, -2.5). You can also think of it as how do you get from A to M. To get from -2 to 3 you add 5. To get from 7 to 4.5 you subtract 2.5
 
 
 

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