Coordinate plane with triangles efg and ghi with e at negative 6 comma 2, f at negative 2 comma 6, g at negative 2 comma 2, h at negative 2 comma 4, and i at 0 comma 2
which set of transformations would prove δefg ~ δghi?
translate δghi by the rule (x − 2, y + 0), and reflect δg′h′i′ over x = −4.
reflect δghi over x = −2, and translate δg′h′i′ by the rule (x − 2, y + 0).
translate δghi by the rule (x + 0, y + 2), and dilate δg′h′i′ by a scale factor of 2 from point h.
reflect δghi over x = −2, and dilate δg′h′i′ by a scale factor of 2 from point g.

Step-by-step explanation:

Without looking at the Answers, what do we have?  Two triangles, one smaller than the other and facing the opposite direction, so we want to fix both of those.  

How do we change the direction one is facing?  That's reflection.  And how do we change size?  Dilation, now which of the choices have both of those?

Of course you should checkt o make sure those transformations work, as this could be a trick question or something.  So, reflecting over x = -2 will keep H and G the same since they are on x = -2, but I will flip to the opposite direction, so check there.  

Now dilation it mentions doing so by a factor of 2 from G.  Thankfully I and H are directly verical and horizontal from G so that's really easy.  H is easy, it is 2 above G so dilating by 2 makes it go to 4, which is exactly where F is.  

I you have to mae sure you reflected first, which changes I to be at (-4,2).  This makes it 2 to the left of G.  Dilating by 2 makes it 4, which again puts it right at E.  Since all the points line up the triangles are similar/ congruent.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.