1.
When dilation is about the origin, every coordinate value is multiplied by the dilation factor. Here, that factor is 3, so every coordinate gets multiplied by 3.
... A'(6,6), B'(6,15), C'(18,15), D'(18,6)
2.
The point of division (P) for directed line segment ST into the ratio a:b is found as ...
... P = (bS +aT)/(a+b)
a) (1·(6, 12) +1·(15, -4))/(1+1) = (21/2, 8/2) = (10.5, 4)
b) (2·(6, 12) +5·(20,12))/(2+5) = (112/7, 84/7) = (16, 12)
c) (3·(20, 12) +2·(15, -4))/(3+2) = (90/5, 28/5) = (18, 5.6)
