This problem has 3 parts. I figured out the answer to a and b. i only need c.
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document.write( "Let A = (-2,3), B = (6,7), and C = (-1,6).
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document.write( "a.) Find an equation for the perpendicular bisector of AB.
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document.write( "My answer is: y= -3x +3
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document.write( "Sorry, that's wrong. Plot the two points:\r\n" );
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document.write( "Find the midpoint using the midpoint formula:\r\n" );
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document.write( "Given the two points (
, 
), (
, 
), \r\n" );
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document.write( "Their midpoint = (
, 
)\r\n" );
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document.write( "Substituting points (-2,3) and (6,7), \r\n" );
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document.write( "Their midpoint = (, )\r\n" );
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document.write( "= (
, 
) = (
, 
) = (
, 
)\r\n" );
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document.write( "So we plot that, and connect the three points:\r\n" );
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document.write( "Next we find the slope of AB using the slope formula:\r\n" );
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document.write( "To find the slope of a line which is perpendicular to \r\n" );
document.write( "a line with slope 
, we invert the fraction and \r\n" );
document.write( "change its sign, and get 
or 
\r\n" );
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document.write( "Now since the line goes through (2,5), we use the point-slope\r\n" );
document.write( "form of a line's equation using 
:\r\n" );
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document.write( "y-5=-2(x-2)\r\n" );
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document.write( "y-5=-2x+4\r\n" );
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document.write( "y=-2x+9\r\n" );
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document.write( "Now we draw that and get:\r\n" );
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document.write( "
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\r
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document.write( "b.) Find an equation for the perpendicular bisector of BC.
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document.write( "y= -3x + 13
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document.write( "Sorry, that's wrong, too Plot the two points:\r\n" );
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document.write( "
\r\n" );
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document.write( "Find the midpoint using the midpoint formula:\r\n" );
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document.write( "Given the two points (, ), (, ), \r\n" );
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document.write( "Their midpoint = (, )\r\n" );
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document.write( "Substituting points (6,7) and (-1,6), \r\n" );
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document.write( "Their midpoint = (, )\r\n" );
document.write( "\r\n" );
document.write( "= (
, 
) = (
, 
) = (
, 
)\r\n" );
document.write( "\r\n" );
document.write( "So we plot that, and connect the three points:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we find the slope of BC using the slope formula:\r\n" );
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document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "To find the slope of a line which is perpendicular to \r\n" );
document.write( "a line with slope 
, we invert the fraction and \r\n" );
document.write( "change its sign, and get 
or 
\r\n" );
document.write( "\r\n" );
document.write( "Now since the line goes through (2.5,7.5), we use the point-slope\r\n" );
document.write( "form of a line's equation using 
:\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "Now we draw that and get:\r\n" );
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document.write( "
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document.write( "c.) Find coordinates for a point K that is equidistant from A, B, and C.
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document.write( "This amounts to finding the center of a circle that passes \r\n" );
document.write( "through all three points, for the center of a circle is\r\n" );
document.write( "equidistant from all points on a circle.\r\n" );
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document.write( "AB and BC are both chords. There is a theorem that says,\r\n" );
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document.write( "\"The perpendicular bisectors of two chords intersect at the\r\n" );
document.write( "center of a circle. \r\n" );
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document.write( "Now we can draw in the circle:\r\n" );
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document.write( "So we solve the system of the equations of the two perpendicular \r\n" );
document.write( "bisectors of the above two problems and we get:\r\n" );
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document.write( "Solve that system of equations by substitution, which I assume\r\n" );
document.write( "you can do, and get\r\n" );
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document.write( "x=3, y=3.\r\n" );
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document.write( "So the point (3,3) is the center of the circle, which is\r\n" );
document.write( "equidistant from all three given points A, B, and C.\r\n" );
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document.write( "Edwin
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