Let R be an extended affine root system in a vector space V. The Weyl group of R is the group generated by reflections based on nonisotropic elements of R. Recently, we found a presentation for the Weyl group of any extended affine root system of type $A_1$, which is very similar to the Coxeter presentation of finite and affine Weyl groups. In this talk, we first discuss a geometric proof of the mentioned presentation and then we talk about a length function on these groups. In the geometric proof, we use paths and loops created by simplices. Loops defined in this way are in a one-to-one correspondence with the relations of the Weyl group. On the other hand, one can define a way to reduce each loop to a "fundamental" loop. These "fundamental" loops are in a one-to-one correspondence with the relations of the Weyl group which we consider for our presentation. We know that Weyl groups of affine Kac-Moody root systems are both Coxeter groups and Weyl groups of extended affine root systems of nullity one. Furthermore, each Coxeter groupi $W$ has a length function which for any element $w \in W$ gives the minimum number of Coxeter generators needed to build $w$. On the other hand, we showed that the Weyl groups of extended affine root systems of type $A_1$ have a "similar" presentation to the affine Coxeter presentation. In order to show that Coxeter groups and these Weyl groups are "related", in the second part of this talk, we discuss a length fucntion for Weyl groups of extended affine root systems of type $A_1$ which is the same as the Coxeter group's length function for Weyl groups of affine Kac-Moody root systems of type $A_1$. Our proof of the existence of this length function uses algebraic, combinatorial and geometric properties of these class of Weyl groups and their underlying root systems. For instance, we define a notion of positive and negative roots on extended affine root systems which is highly connected to the length function of the corresponding Weyl groups.