What are the coordinates of E' that will justify ∆DEF ~ ∆D'E'F'?

Question

The transformation of ∆DEF is described in the table.

∆DEF∆D'E'F'
D (0, 0)	D' (0, 0)
E (3, 2)	E' (x, y)
F (7, 6)	F' (14, 12)

What are the coordinates of E' that will justify ∆DEF ~ ∆D'E'F'? 

1. (5, 4) 
2. (6, 4)
3.  (9, 6) 
4. (12, 10)

Answer 1

Comparing sides DF and D'F', we see that this is a dilation by a factor of 2 in the horizontal dimension.

Comparing sides DF and D'F', we see that this is also a dilation by a factor of 2 in the vetical dimension.

So, if we dilate the vertical and horizontal components of (3,2) by a factor of 2, we obtain (6,4). So the correct answer is choice (2) above.