document.write( "Question 257290: Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of point B so that the line x-2 is the perpendicular bisector of AB \n" ); document.write( "
Algebra.Com's Answer #189503 by dabanfield(803)\"\" \"About 
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Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of point B so that the line x-2 is the perpendicular bisector of AB\r
\n" ); document.write( "\n" ); document.write( "The line y = x - 2 is in slope-intercept form so has a slope of 1. The line passing througth (-4,1) which is perpendicular to this line must have a slope which is the negative reciprocal of 1 which is -1/1 = -1. \r
\n" ); document.write( "\n" ); document.write( "So the equation of the perpendicular line in slope-intercept form is\r
\n" ); document.write( "\n" ); document.write( "y = -1*x + b\r
\n" ); document.write( "\n" ); document.write( "Since (-4,1) is on this line we have:\r
\n" ); document.write( "\n" ); document.write( "1 = -1*-4 + b
\n" ); document.write( "b = -3\r
\n" ); document.write( "\n" ); document.write( "The equation of the perpendicular line is then:\r
\n" ); document.write( "\n" ); document.write( "y = -x - 3\r
\n" ); document.write( "\n" ); document.write( "To see where the two lines intersect we need to simulaneously solve:\r
\n" ); document.write( "\n" ); document.write( "1.) y = -x - 3
\n" ); document.write( "2.) y = x - 2 \r
\n" ); document.write( "\n" ); document.write( "Substitute x-2 in equation 1.):\r
\n" ); document.write( "\n" ); document.write( "x - 2 = -x - 3
\n" ); document.write( "2x = -1
\n" ); document.write( "x = -1/2 (the x-coordinate of B)\r
\n" ); document.write( "\n" ); document.write( "Substitute -1/2 for x in 2.) above to get the value of y for point B. \r
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