Answer:
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
