Given abcd ~ efgh, what is fg?
a.3.6

b.4.5

c.8

d.10

B. 4.5

Step-by-step explanation:

Since the are similar quadrilaterals, their side lengths are in proportion to each other.

Look at the letter ordering, ABCD   and EFGH,   the represent corresponding points in the quadrilateral, so  

BC and FG are the same corresponding side of the quadrilateral.  For the first quadrilateral, A is the first letter, B is the second. In the second quadrilateral, E is the first letter, and F is the second.  A corresponds to E, and B corresponds to F.  The rest of the letters correspond the same way

as are CD and GH

So we have a proportion, "CD is to GH as BC is to FG"

We have values for all sides in our proportion except FG, so plug them in...

CD =4, GH = 6, BC = 3 and FG is unknown,

4/6 = 3/FG

Solve for FG by cross-multiplying (here FG is one variable)

4FG = 18

  FG = 18/4

     FG = 4.5

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

yes.. it's proven to be 36.