Question 956938: Help please.
The point G(5,-9) is rotated 90 degrees about point M(-8,3) and then reflected across the line y=9. Find the coordinates of the image G'.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website!
Let's switch coordinates and look at G using M as (0,0).
From M to G, the x distance is 
and the y distance is 
So in M coordinates, G is (13,-12).
To rotate about M by 90 degrees then G becomes (12,13) or (-12,-13) depending on positive or negative rotation by 90, since you didn't specify.
Remember these are in M coordinates.
So to change back to the original coordinates, we have to add back the coordinates of M.
(12,13)+(-8,3)=(4,16)
(-12,-13)+(-8,3)=(-20,-10)
So now if we reflect about  , you find the y-distance from and then add that distance to 9 to get the new y-coordinate.
So for (4,16), the distance from is  .
Since the point is above , we will subtract 7 from the to get the reflected point.
(4,9-7)=(4,2)
and for (-20,-10), the distance to is  so then add 19 to
(-20,9+19)=(-20,28)
So then G' is either (4,2) or (-20,28).
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