How to Rotate a "Street" correctly

Hi guys, i am working on a Sub-System, a road creation in a simCity way. i am in a phase of experimentation, i know the basics, so here is my question. i am using a function named mousePosition,with raycasting. i create a mesh dinamicaly(4 vertices), The idea is simple, i made 1 click and CreateRoad is called. The center of the mesh is exactly where the mouse was clicked. the road lenght is 4. Alpha(4Pix)-------Beta(0pix)
imagine the road with both extremes Alpha and Beta. the center is on B. i want to rotate Alpha toward the mouse location. point Beta must be fixed and A always have to be looking at mouse location. My problem is that my road rotates with Beta looking the mouse location, not Alpha.The road rotates complete, not with a fixed point. i have tried to add a GameEmpty like a parent but i cant separate the Transform from the road mesh becouse there is no option to do this from Unity. i have tried a lot of codes and i dont get it to work, i have readed a lot of post too. here is the complete script with comments. i would love to know if somebody knows how to do it correctly. Thanks a lot, and hope you understand my question. Image beneath.

using UnityEngine; using System.Collections;

public class GroundClick : MonoBehaviour {

 public GameObject prefabRoad;
 public GameObject nodeRotation;
 public GameObject prefabNode;


 float lenght;
 Vector3 roadEnd;
 Vector3 roadStart;
 Vector3 lookAtRoad;
 float width;
 Mesh mesh;
 bool boton;
 GameObject road;
 RaycastHit hitinfo ;
 Ray ray;
 MeshFilter mesh_filter;
 int creandoCalle;  //si vale 1 se dio un click y se esta posicionando la calle
                     // si vale 2 se dio el segundo click y se lo pone definitivamente
                     //si vale cero no se hizo click sobre crear calle

 
 
 
 void Start(){
     creandoCalle=0;
 }

 
 
 void Update () {
     
         if(Input.GetMouseButtonDown(0))
         {
             getClickLocation(out roadStart);
             createRoad(roadStart);

             creandoCalle=1;
         }

         if(creandoCalle==1){
             rotate();
         }
     
 }


 void rotate()
 {

     getClickLocation(out lookAtRoad); //obtain the mouse position and saves it on LookAtRoad
     Debug.Log(lookAtRoad);

             //Quaternion rot=Quaternion.LookRotation(lookAtRoad);
             //rot*= Quaternion.Euler(new Vector3(0,0,0));
             //road.transform.rotation=Quaternion.Slerp(road.transform.rotation,rot,Time.deltaTime*100);
             
             //road.transform.rotation= Quaternion.RotateTowards(road.transform.rotation,rot,1);
             //road.transform.rotation=Quaternion.FromToRotation(road.transform.position,lookAtRoad.normalized);
             //road.transform.RotateAround(road.transform.forward*new Vector3(0,0,4),new Vector3(0,0,1),Quaternion.Angle(road.transform.rotation,))
 road.transform.LookAt(lookAtRoad);
             //road.transform.rotation=Quaternion.FromToRotation(road.transform.position,lookAtRoad);
             //road.transform.Rotate
 }

 void TerminarTramoDeCalle ()
 {

 }
 
 bool getClickLocation(out Vector3 point)
 {
     ray=Camera.main.ScreenPointToRay(Input.mousePosition);
     hitinfo =new RaycastHit();
     if(collider.Raycast(ray,out hitinfo, Mathf.Infinity)){
         point =hitinfo.point;
         return true;
     }
     point= Vector3.zero;
     return false;
 }
 
 
 void createRoad(Vector3 roadStart){
     
     road= Instantiate(prefabRoad) as GameObject;
     
     road.transform.position =  roadStart+ new Vector3(0,0.01f,0);
     //road.transform.rotation= Quaternion.FromToRotation(roadStart, roadEnd);
     width=1;
     lenght=4;
     
     Vector3[] vertices = new Vector3[]
     {
         new Vector3( 1, 0, 1),
         new Vector3( 1, 0, -5),
         new Vector3(-1, 0, 1),
         new Vector3(-1, 0, -5),
     };

     int[] triangles = new int[]
     {
         0, 1, 2,
         2, 1, 3,
     };
     Vector2[] uv = new Vector2[]
     {
         new Vector2(1, 1),
         new Vector2(1, 0),
         new Vector2(0, 1),
         new Vector2(0, 0),
     };

     Vector3[] normals={
         Vector3.up,
         Vector3.up,
         Vector3.up,
         Vector3.up
             
     };
     
     mesh= new Mesh();
     mesh.vertices=vertices;
     mesh.triangles=triangles;
     mesh.uv=uv;
     
     mesh.normals=normals;
     
     mesh_filter=road.GetComponent<MeshFilter>();
     mesh_filter.mesh=mesh;

 }
 
 

}

i have tried a lots of code that doesnt work properly.