In general, the origin of the new object is the same because the scalation is made by using the origin of the previous object as a fixed point.
The dimensions of the new object are found simply by multiplying each coordinate of special points of the object by the scale factor.
For example, if the points (x1,y1), (x2,y2) and (x3,y3) are vertices of an object with triangle shape, the new object will have the coordinates
(k*x1,k*y1), (k*x2,k*y2) and (k*x3,k*y3) where the scale factor is k.