Randomising array coordinates with no duplicates AS3

very new to this kind of thing so please bear with me.

So basically I have 4 buttons that I have put to the stage using the Actions panel. They all have set coordinates so every time I run my game, they are in the same place.

Now here's my issue, I want these buttons to randomise their positions using those coordinates, but I often get duplicates, meaning one button is on top of another.

Here is my code so far

var coordArray : Array = [
              new Point(44,420),
              new Point(270,420),
              new Point(44,550),
              new Point(270,550),

              ];            

var pointRange:Number = 4;
var randomPoint:int = Math.random()*pointRange;
answerButtons.x = coordArray[randomPoint].x;
answerButtons.y = coordArray[randomPoint].y;    

var pointRange_2:Number = 4;
var randomPoint_2:int = Math.random()*pointRange_2;
answerButtons_2.x = coordArray[randomPoint_2].x;
answerButtons_2.y = coordArray[randomPoint_2].y;

var pointRange_3:Number = 4;
var randomPoint_3:int = Math.random()*pointRange_3;
answerButtons_3.x = coordArray[randomPoint_3].x;
answerButtons_3.y = coordArray[randomPoint_3].y;

var pointRange_4:Number = 4;
var randomPoint_4:int = Math.random()*pointRange_4;
answerButtons_4.x = coordArray[randomPoint_4].x;
answerButtons_4.y = coordArray[randomPoint_4].y;

I have googled this profusely and I keep getting answers to do with the splice and shift methods. Is this the type of thing I need? I'm assuming I need a function that removes a point from the array after it is used.

Cheers.