Answer: (-1, -5)
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Step-by-step explanation
The center of dilation is (-7,-7) which is not the origin.
Move the point 7 units right and 7 units up to move this center to the origin.
It means we'll move W(8,-2) along this pathway as well to arrive at (15,5)
Then multiply the scale factor 2/5 with each coordinate.
- 15*(2/5) = 30/5 = 6
- 5*(2/5) = 10/5 = 2
The point (15,5) scales down to (6,2)
Lastly, we move that point 7 units left and 7 units down to undo the previous translation applied. This is to return the center of dilation back to (-7,-7).
We move (6,2) seven units left and seven units down to arrive at (-1, -5) which is the location of point W'.
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Another approach
To go from (-7,-7) to (8,-2) we follow this pathway: go right 15, go up 5.
Take 2/5 of 15 and 5 to get 6 and 2. See the previous section above for those calculations.
We'll start at (-7,-7) and move right 6 then up 2 to arrive at (-1, -5) which is the final answer.