document.write( "Question 992821: Hi, I need help solving this : Find the point (x, y) on the line y=x that is equidistant from the points (8, 9) and (1, -10), thank you! \n" ); document.write( "

Algebra.Com's Answer #612314 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "This point has coordinates (x,x) with the unknown x,\r
\n" ); document.write( "\n" ); document.write( "and the equation to find x is the equality of distances \r
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\n" ); document.write( "\n" ); document.write( "from (x,x) to (8,9): $\"sqrt%28%288-x%29%5E2+%2B+%289-x%29%5E2%29%29\"$ , and\r
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\n" ); document.write( "\n" ); document.write( "from (x,x) to (1, -10): $\"sqrt%28%281-x%29%5E2+%2B+%28-10-x%29%5E2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "This equation is (after squaring the square roots):\r
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\n" ); document.write( "\n" ); document.write( " $\"%288-x%29%5E2+%2B+%289-x%29%5E2%29\"$ = $\"%281-x%29%5E2+%2B+%28-10-x%29%5E2%29\"$ , or\r
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\n" ); document.write( "\n" ); document.write( " $\"64+-16x+%2B+x%5E2\"$ + $\"81+-+18x+%2B+x%5E2\"$ = $\"1+-+2x+%2B+x%5E2\"$ + $\"100+%2B+20x+%2B+x%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Simplify and solve it.\r
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\n" ); document.write( "\n" ); document.write( "64 + 81 -1 - 100 = 16x + 18x - 2x + 20x,\r
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\n" ); document.write( "\n" ); document.write( "44 = 52x\r
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\n" ); document.write( "\n" ); document.write( "x = $\"44%2F52\"$ = $\"11%2F13\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Answer. The point is ( $\"11%2F13\"$ , $\"11%2F13\"$ ).\r
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