document.write( "Question 1203788: Find the point (𝑥,𝑦) on the line 𝑦=−2𝑥+4
\n" ); document.write( "that is equidistant from the points (8,−3) and (−5,−10) \n" ); document.write( "

Algebra.Com's Answer #839629 by MathLover1(20850) $\"\"$ $\"About$

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given:\r
\n" ); document.write( "\n" ); document.write( "the points ( $\"+8\"$ , $\"+-3\"$ ) and ( $\"+-5\"$ , $\"+-10\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"+y=+-2x%2B4\"$ .........eq.1\r
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\n" ); document.write( "\n" ); document.write( "using distance formula\r
\n" ); document.write( "\n" ); document.write( "distance from ( $\"x\"$ , $\"y\"$ ) to ( $\"8\"$ , $\"-3\"$ ) is equal to distance from ( $\"x\"$ , $\"y\"$ ) to ( $\"-5\"$ , $\"-10\"$ ) \r
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\n" ); document.write( "\n" ); document.write( " $\"%28-9+-+x%29%5E2+%2B+%287+-+y%29%5E2+=+%28-8+-+x%29%5E2+%2B+%28+3+-+y%29%5E2\"$
\n" ); document.write( " $\"%288+-+x%29%5E2+%2B+%28-3+-+y%29%5E2+=+%28-5+-+x%29%5E2+%2B+%28+-10+-+y%29%5E2+\"$
\n" ); document.write( " $\"y+=+-%2813+x%29%2F7+-+26%2F7\"$ .........eq. 2\r
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\n" ); document.write( "\n" ); document.write( " equal eq.1 and eq.2\r
\n" ); document.write( "\n" ); document.write( " $\"-2x+%2B+4=+-%2813+x%29%2F7+-+26%2F7\"$ ....solve for $\"x\"$
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\n" ); document.write( " $\"x+=+54\"$ \r
\n" ); document.write( "\n" ); document.write( "plug in $\"y=+-2x%2B4\"$ ----eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"y=+-2%2A54%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=-104\"$ \r
\n" ); document.write( "\n" ); document.write( "so, point is\r
\n" ); document.write( "\n" ); document.write( "( $\"x\"$ , $\"y\"$ )=( $\"54\"$ , $\"-104\"$ )\r
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\n" ); document.write( "\n" ); document.write( "check: if the distances of ( $\"54\"$ , $\"-104\"$ ) from ( $\"8\"$ , $\"-3\"$ ) and ( $\"-5\"$ , $\"-10\"$ ) are same\r
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\n" ); document.write( "\n" ); document.write( "the distances of ( $\"54\"$ , $\"-104\"$ ) from ( $\"8\"$ , $\"-3\"$ ) is $\"sqrt%2812317%29\"$ ≈ $\"110.982\"$
\n" ); document.write( "the distances of ( $\"54\"$ , $\"-104\"$ ) from ( $\"-5\"$ , $\"-10\"$ )
\n" ); document.write( " is $\"sqrt%2812317%29\"$ ≈ $\"110.982\"$ \r
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