document.write( "Question 1106795: the equation of a line 3x-2y=20 what point on the line is equidistant from the points A(1,-1) and B(1,8) \n" ); document.write( "

Algebra.Com's Answer #721777 by ikleyn(52910) $\"\"$ $\"About$

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\n" ); document.write( "the equation of a line 3x-2y=20 what point on the line is equidistant from the points A(1,-1) and B(1,8)
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document.write( "The point under the question is the intersection point of the given line with the perpendicular bisector to the line segment\r\n" );
document.write( "connecting the given points A(1,-1)  and  B(1,8). \r\n" );
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document.write( "Notice that the line connecting these points is VERTICAL line x = 1.\r\n" );
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document.write( "Hence, the perpendicular bisector is the horizontal line  y = 3.5   (where 3.5 =  ).\r\n" );
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document.write( "The intersection point is that you will obtain after substituting y = 3.5 into the equation of the given line:\r\n" );
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document.write( "3x - 2y = 20  at  y = 3.5  becomes  3x - 2*3.5 = 20  ====>  3x = 20+7 = 27  ====>  x =  = 3.\r\n" );
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document.write( "Hence, the point you are seeking for is (2,3.5).\r\n" );
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document.write( "Thus you can solve this problem  MENTALLY,  without solving ANY equations.\r\n" );
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