VTMO 2016 — Grade 8 — final Question 5

Rectangle $ABCD$ has $AB = 5 , BC = 2$. $M$ lies on $AB$ with $AM = 1 , N$ on $DC$ with $DN = 2$. $E$ is $D$ reflected in $M , F =$ EN $\cap CM$. $a$)Prove $CM \perp DM$. $b$)For $K = DF \cap CE$, find $DK$.