The simple code looks like this:
copiedDisplayObject.scaleY = -1;
copiedDisplayObject.alpha = 0.4;
That is really a specific example of reflection over a line, where the line happens to be the x axis. (ie y = 0x + 0) If you want to reflect over another line, you can use a matrix. The code below preserves previous transformations on the display object, and reflects it over a line passing through the origin.
var m:Number = 0.25; //example slope -- from line: y = mx + 0
var tmpMatrix = copiedDisplayObject.transform.matrix;
var relectMatrix:Matrix = new Matrix(1-m*m, 2*m, 2*m, m*m -1);
tmpMatrix.concat(relectMatrix);
copiedDisplayObject.transform.matrix = tmpMatrix;
I found the matrix formula here: math.stackexchange question.