document.write( "Question 1053446: reflect (4,-4) over y=3/4x-2 \n" ); document.write( "

Algebra.Com's Answer #668691 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
any line perpendicular to the line
\n" ); document.write( " $\"+y+=+%283%2F4%29%2Ax+-+2+\"$ will have slope=
\n" ); document.write( " $\"+-1%2Fm+=+-1%2F%283%2F4%29+\"$
\n" ); document.write( " $\"+-1%2Fm+=+-4%2F3+\"$
\n" ); document.write( "------------------
\n" ); document.write( "The equation of the line through (4,-4)
\n" ); document.write( "and perpendicular to the given line is:
\n" ); document.write( " $\"+%28+y+-+%28-4%29+%29+%2F+%28+x+-+4+%29+=+-4%2F3+\"$
\n" ); document.write( " $\"+y+%2B+4+=+%28-4%2F3%29%2A%28+x+-+4+%29+\"$
\n" ); document.write( " $\"+y+=+%28-4%2F3%29%2Ax+%2B+16%2F3+-+4+\"$
\n" ); document.write( " $\"+y+=+%28-4%2F3%29%2Ax+%2B+4%2F3+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "Find the point of intersection of the 2 lines
\n" ); document.write( " $\"+%283%2F4%29%2Ax+-+2+=+%28-4%2F3%29%2Ax+%2B+4%2F3+\"$
\n" ); document.write( "Multiply both sides by $\"+12+\"$
\n" ); document.write( " $\"+9x+-+24+=+-16x+%2B+16+\"$
\n" ); document.write( " $\"+25x+=+40+\"$
\n" ); document.write( " $\"+x+=+8%2F5+\"$
\n" ); document.write( "---------------
\n" ); document.write( "Plug this result back into the original equation
\n" ); document.write( " $\"+y+=+%283%2F4%29%2Ax+-+2+\"$
\n" ); document.write( " $\"+y+=+%283%2F4%29%2A%288%2F5%29+-+10%2F5+\"$
\n" ); document.write( " $\"+y+=+6%2F5+-+10%2F5+\"$
\n" ); document.write( " $\"+y+=+-4%2F5+\"$
\n" ); document.write( "The intersection is at ( 8/5, -4/5 )
\n" ); document.write( "Make this the midpoint of the reflected points
\n" ); document.write( " $\"+%28+x+%2B+4+%29+%2F+2+=+8%2F5+\"$
\n" ); document.write( " $\"+5%2A%28+x+%2B+4+%29+=+2%2A8+\"$
\n" ); document.write( " $\"+5x+%2B+20+=+16+\"$
\n" ); document.write( " $\"+5x+=+-4+\"$
\n" ); document.write( " $\"+x+=+-4%2F5+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+%28+y+%2B%28-4%29+%29+%2F+2+=+-4%2F5+\"$
\n" ); document.write( " $\"+%28+y+-+4+%29+%2F+2+=+-4%2F5+\"$
\n" ); document.write( " $\"+5%2A%28+y+-+4+%29+=+-8+\"$
\n" ); document.write( " $\"+5y+-+20+=+-8+\"$
\n" ); document.write( " $\"+5y+=+12+\"$
\n" ); document.write( " $\"+y+=+12%2F5+\"$
\n" ); document.write( "------------------
\n" ); document.write( "The reflected point is ( -4/5, 12/5 )
\n" ); document.write( "-----------------------------------
\n" ); document.write( "Here's the plot of the 2 lines:
\n" ); document.write( "

\n" ); document.write( "Looks like my answer can be correct\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );