document.write( "Question 1203373: The point $(x,y)$ in the coordinate has a distance of $6$ units from the $x$-axis, a distance of $15$ units from the point $(5,7)$, and a distance of $\sqrt{n}$ from the origin. If both $x$ and $y$ are negative, what is $n$? \n" ); document.write( "

Algebra.Com's Answer #838879 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "given:\r
\n" ); document.write( "\n" ); document.write( "the distance between ( $\"+x\"$ , $\"++y\"$ ) and the $\"+x\"$ -axis is $\"+6\"$ units.\r
\n" ); document.write( "\n" ); document.write( "The nearest point to ( $\"+x\"$ , $\"++y\"$ ) in the $\"+x\"$ -axis is the point ( $\"+x\"$ , $\"+0\"$ ) so we have:\r
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\n" ); document.write( "\n" ); document.write( " $\"+6+=+sqrt%28+%28x+-+x%29%5E2+%2B+%28y+-+0%29%5E2%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28y%5E2%29=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"abs%28y%29+=+6%7C%7C%7C%0D%0A%0D%0A%0D%0Aso+%7B%7B%7B+y\"$ can be $\"+6\"$ or $\"+-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "So we know that $\"x\"$ and $\"y\"$ are negative, our point will be in Q III.\r
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\n" ); document.write( "\n" ); document.write( "so, $\"+y=-6\"$ and now we can write our point as ( $\"+-x\"$ , $\"+-6\"$ )\r
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\n" ); document.write( "\n" ); document.write( " the distance between our point and ( $\"+5\"$ , $\"+7\"$ ) is $\"+15\"$ units:\r
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\n" ); document.write( "\n" ); document.write( " $\"+sqrt%28+%28x+-+5%29%5E2+%2B+%28y+-+7%29%5E2%29+=+15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+x+=+5+-+2+sqrt%2814%29\"$ \r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"+x+=+5+%2B+2+sqrt%2814%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "And we know that the distance from the origin, ( $\"+0\"$ , $\"+0\"$ ) is $\"+sqrt%28n%29+\"$ :\r
\n" ); document.write( "\n" ); document.write( " $\"+sqrt%28n+%29=+sqrt%28x%5E2+%2B+y%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+n+=x%5E2+%2B+y%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+n+=+%285+-+2sqrt%2814%29%29%5E2+%2B+%28-6%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+n+=+42.2\"$ (approximately) \r
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