document.write( "Question 1182539: Q is the rotation of P(8,1) counter clockwise through 90* about the origin O, i.e. OP=OQ and angle QOP=90*. R Is the reflection of Q in the line y=x. S is the reflection of R in the y-axis. Find the coordinates of S. \n" ); document.write( "
Algebra.Com's Answer #812616 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Refer to this handy chart
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\n" ); document.write( "(image source: OnlineMath4all.com)\r
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\n" ); document.write( "\n" ); document.write( "The chart tells us that P(8,1) rotates to Q(-1,8)
\n" ); document.write( "We use the rule in the second row telling us (x,y) rotates to (-y,x) when doing a 90 degree counter-clockwise rotation.
\n" ); document.write( "We swap the x and y coordinates, then make the first coordinate (after the swap) the opposite sign of what it was before.\r
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\n" ); document.write( "\n" ); document.write( "Now, we apply a reflection over the line y = x
\n" ); document.write( "The rule is that any (x,y) point reflects to (y,x). The x and y coordinates swap. There are no sign changes here.
\n" ); document.write( "Q(-1,8) reflects to R(8,-1)\r
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\n" ); document.write( "\n" ); document.write( "When applying a y axis reflection, we change the sign on the x coordinate but the y coordinate stays the same.
\n" ); document.write( "In general, we go from (x,y) to (-x,y)
\n" ); document.write( "Specifically, R(8,-1) reflects to S(-8,-1)\r
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\n" ); document.write( "\n" ); document.write( "Answer: (-8,-1)\r
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\n" ); document.write( "\n" ); document.write( "Diagram:
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\n" ); document.write( "I used GeoGebra to make the diagram.
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