How can I move an UI Image to a touch position?

I have an image on the scene. Now when I touch on my mobile device to a specific position, I want, that the image moves to this position.

How can I do it?

I wrote this:

transform.position = Input.mousePosition;

But this don't work. Ok, it's working, but the image is not anymore on the screen. It's somewhere on the right side.

I found this. But it's also not working:

gameObject.GetComponent<RectTransform>().localPosition = new Vector2(Input.mousePosition.x, Input.mousePosition.y);

Here is the problem, that when I touch on the screen bottom left (mobile) the object is in the center of the screen.

You can move the UI Image by putting the following in a script attached to it:

void Update() {

    for (var i = 0; i < Input.touchCount; i++) {

        if (Input.GetTouch(i).phase == TouchPhase.Began) {

            // assign new position to where finger was pressed
            transform.position = new Vector3 (Input.GetTouch(i).position.x Input.GetTouch(i).position.y, transform.position.z);

        }

    }    

}