Question

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Answer 1

So, I haven't really done this stuff to a point that I can be certain, so you may have to look over this a few times in case I messed something up or maybe it does sound correct... Sorry. I just want to give you "an" answer to see.


What I did, was I took the points of the solid triangle and then of the dashed triangle:
(-6,0), (6,3), (6,-6) --> (-2,0), (2,1), (2,-2)
Now, intuitively, I can see that there's something going on between these points. They all match this pattern:
(x,y) --> (1/3 x, 1/3 y)
This suggests to me that the scale factor is 1/3, because the points are always getting scaled down by 1/3. (-6/3,0/3) = (-2,0); (6/3, 3/3) = (2,1), (6/3, -6/3) = (2,-2).
Also, since the new point is an exact scaling down of the points (they're not moved at all with respect to the original), it seems like the center is (0,0).

Answer 2

For #2, I believe we would find the coordinates and multiply both the x and y by 4.
A(-3,1) --> A'(4* -3, 4* 1) = A'(-12,4)
B(4,-3) ---> B'(4*4, 4*-3) = B'(16,-12)
C(2,3) and so on like that ^
D(-1,4)

Answer 3

It looks to me like, you can actually show that the center is at (0,0) just by drawing a line through from the original vertex to the new vertex