document.write( "Question 334746: The midpoint of segment AB is (0,1/2). if endpoint A is (2,-2), find the coordinates of endpoint B. \n" ); document.write( "

Algebra.Com's Answer #239860 by Edwin McCravy(20056) $\"\"$ $\"About$

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Two ways to do this. Graphically and algebraically.
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document.write( "Graphical method:\r\n" );
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document.write( "Call the midpoint \r\n" );
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document.write( "Draw a green line from A(2,-2) left horizontally until you \r\n" );
document.write( "are directly underneath the midpoint .  That \r\n" );
document.write( "requires you to draw the green line 2 units left.  \r\n" );
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document.write( "Now from the end of the green line, draw a vertical \r\n" );
document.write( "green line upward to point . That \r\n" );
document.write( "requires you to draw the vertical green line  units \r\n" );
document.write( "directly upward.  \r\n" );
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document.write( "Draw a green line from  left 2 units \r\n" );
document.write( "horizontally, the same number of units left that we\r\n" );
document.write( "drew the other horizontal line. That puts you directly\r\n" );
document.write( "above -2 on the x-axis.\r\n" );
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document.write( "Now from the end of that green line, draw a green line \r\n" );
document.write( "directly upward  units vertically, the same \r\n" );
document.write( "number of units left that we drew the other vertical \r\n" );
document.write( "line. That puts you directly above -2 on the x-axis.\r\n" );
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document.write( "Now we can extend AM to B, and we now have AB.  And we see \r\n" );
document.write( "that B is the point B(-2,3)\r\n" );
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document.write( "By algebra:\r\n" );
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document.write( "Use the midpoint formula:\r\n" );
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document.write( "The midpoint between  and \r\n" );
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document.write( "So\r\n" );
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document.write( "The midpoint between  and \r\n" );
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document.write( "So\r\n" );
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document.write( "So we set the x-coordinates equal:\r\n" );
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document.write( "Multiply both sides by 2\r\n" );
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document.write( "And we set the y-coordinates equal:\r\n" );
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document.write( "Multiply both sides by 2\r\n" );
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document.write( "So B has the coordinates \r\n" );
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document.write( "Edwin

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