When scaling a plane around a point, the result is a plane of a different size but the same shape.
It is highly-recommended to draw everything out.
SCALING FROM A CENTERPOINT
Scaling is commonly done about (0,0), in which case it looks like this:
and you can see that the z-axis (into/out of the screen, or in the hatk direction) would pass through the exact centers of both triangles DeltaABC and DeltaA'B'C'.
In this scenario, it is clearer what has happened to each point. A("-2,-2") has been scaled outwards by a factor of 2 to achieve A'("-4,-4"), B("1,1") has been scaled outwards by a factor of 2 to achieve B'("2,2"), and C("0,2") has been scaled outwards by a factor of 2 to achieve C'("0,4").
In general, scaling about a central point is given as:
color(blue)(P'(x,y) = P(kx,ky) " where " k in RR " and " k > 0)
SCALING OFF-CENTER
Scaling might also be done from an arbitrary non-central point. For instance, scaling a triangular plane D_k outwards from point O by non-zero scalar k in RR where k = (OA')/(OA) = (OB')/(OB) = (OC')/(OC) gives the transformation
for which A, B, and C were points on the green triangle. In this case, the scaling shrunk DeltaABC into DeltaA'B'C' by a factor of k where 0 < k < 1.
You can see that DeltaABC and DeltaA'B'C' expand along the axes that pass through points O, as well as A, B, C, A', B', or C'.
