2d - How do I make an object face the mouse position, but only on one plane?

I want a game object to turn and look towards where the mouse was clicked (in world space). It works well when considering all 3 dimensions, but I really only care for the plane formed by the x and z axis, not the y.

I've tried to fix this by setting the y of the directionTarget to the y of the object's position, but that gives weird results.

My code looks like this:

Quaternion rotationTarget;
    float rotationLerpProgress;
    float rotationLerpDuration = 1f;


    // Use this for initialization
    void Start ()
    {

    }

    // Update is called once per frame
    void Update ()
    {
            if (Input.GetMouseButtonDown (0)) {

                    var ray = Camera.main.ScreenPointToRay (Input.mousePosition);
                    RaycastHit rayHit; 
                    if (Physics.Raycast (ray, out rayHit)) {
                            var rayHitPoint = rayHit.point; 
                            var rotationDirection = transform.position - rayHitPoint;                               
                            rotationDirection.Normalize ();
                            //rotationDirection.y = transform.position.y;
                            rotationTarget = Quaternion.LookRotation (rotationDirection);
                            rotationLerpProgress = Time.deltaTime;
                    }

                    //targetPosition = Camera.main.ScreenToWorldPoint (Input.mousePosition);                        
            }

            if (rotationTarget != transform.rotation) {

                    transform.rotation = Quaternion.Lerp (transform.rotation, rotationTarget, rotationLerpProgress / rotationLerpDuration);
                    rotationLerpProgress += Time.deltaTime; 

                    if (rotationLerpProgress >= rotationLerpDuration) {


                            transform.rotation = rotationTarget;
                    }

            }

    }

I must be missing something. How do I do this right?

Answer

I'd project the rotationDirection into the horizontal plane before you normalize it, something like...

var rotationDirection = transform.position - rayHitPoint; 

rotationDirection.y = 0;

rotationDirection.Normalize ();
rotationTarget = Quaternion.LookRotation (rotationDirection);

Note that the order of the subtraction used to define your rotationDirection there results in a vector from the rayHitPoint to transform.position, not the other way - is that as intended?