document.write( "Question 723024: Point A(1,4)is equidistant from the
\n" ); document.write( "points (k,-2) and (4,k).find the value of
\n" ); document.write( "K \n" ); document.write( "

Algebra.Com's Answer #442990 by mananth(16946) $\"\"$ $\"About$

You can put this solution on YOUR website!
Point A(1,4)is equidistant from the
\n" ); document.write( "points P(k,-2) and Q(4,k).find the value of
\n" ); document.write( "K \r
\n" ); document.write( "\n" ); document.write( "use the distance formula\r
\n" ); document.write( "\n" ); document.write( "d(AP) = $\"sqrt%28%28k-1%29%5E2%2B%28-2-4%29%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "d(AQ) = $\"sqrt%28%284-1%29%5E2%2B%28k-4%29%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "d(AP) = d(AQ)\r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28%28k-1%29%5E2%2B%28-2-4%29%5E2%29\"$ = $\"sqrt%28%284-1%29%5E2%2B%28k-4%29%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Take the square of both sides\r
\n" ); document.write( "\n" ); document.write( " $\"%28%28k-1%29%5E2%2B%28-2-4%29%5E2%29\"$ = $\"%28%284-1%29%5E2%2B%28k-4%29%5E2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"k%5E2-2k%2B1%2B36=9%2Bk%5E2-8k%2B16\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "simplify
\n" ); document.write( "6k=-12
\n" ); document.write( "k=-2\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );