BRANLIEST+15Pts Need help! In each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained.

With a center of (2, -2) the dilation coefficient is 3

Lt me know if I can explain any part more to help you understand.  

Step-by-step explanation:

To get the coefficient we want to see where the points start and where they end up.  it is difficult to tell the exact point of E and G and their transformations, so we will only use H and F and their transformations.  We do need 2 to get the center.

From now on I will only be oooking at y values since we know the center x value.

We know the center has to be between 0 and - 3 because it has to be inside of both shapes.

we also know that the distance from the center point to H is c - 0 and F is c - (-3).

then we also know the same number is multiplying these distances to get the new coordinates, 4 and -5 rspectively.  or more accurtely, the distance is being multiplied by the same number.

This allows us to form some proportions.  namely (c-0)/(c-4) = (c+3)/(c+5)  Solving for c, which is easier than it looks like it might be, gets us c = -2, which is the y coordiante of the center point.

So the center point is (2, -2)

Now finding the dilation coefficient is pretty simple.  How much is each original point multiplied y to get the new point.  To get this there are a few ways.  I am just going to calculate what gets us from one distance to the other.  One distance is 2 to 6 and the other is 1 to 3.  So the answer is 3.

So with a center of (2, -2) the dilation coefficient is 3

7

step-by-step explanation:

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