document.write( "Question 956938: Help please.\r
\n" ); document.write( "\n" ); document.write( "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'. \n" ); document.write( "
Algebra.Com's Answer #584686 by Fombitz(32388)\"\" \"About 
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\n" ); document.write( "Let's switch coordinates and look at G using M as (0,0).
\n" ); document.write( "From M to G, the x distance is \"5-%28-8%29=13\"
\n" ); document.write( "and the y distance is \"-9-3=-12\"
\n" ); document.write( "So in M coordinates, G is (13,-12).
\n" ); document.write( "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.
\n" ); document.write( "Remember these are in M coordinates.
\n" ); document.write( "So to change back to the original coordinates, we have to add back the coordinates of M.
\n" ); document.write( "(12,13)+(-8,3)=(4,16)
\n" ); document.write( "(-12,-13)+(-8,3)=(-20,-10)
\n" ); document.write( "So now if we reflect about \"y=9\", you find the y-distance from \"y=9\" and then add that distance to 9 to get the new y-coordinate.
\n" ); document.write( "So for (4,16), the distance from \"y=9\" is \"16-9=7\".
\n" ); document.write( "Since the point is above \"y=9\", we will subtract 7 from the \"y=9\" to get the reflected point.
\n" ); document.write( "(4,9-7)=(4,2)
\n" ); document.write( "and for (-20,-10), the distance to \"y=9\" is \"9-%28-10%29=19\" so then add 19 to \"y=9\"
\n" ); document.write( "(-20,9+19)=(-20,28)
\n" ); document.write( "So then G' is either (4,2) or (-20,28).
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