document.write( "Question 256075: Please help me with this
\n" ); document.write( " Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB? \n" ); document.write( "

Algebra.Com's Answer #188243 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

is a vertical line. Therefore the line containing the segment AB must be a horizontal line. All points in any horizontal line have identical

coordinates. Therefore, since the

-coordinate of A(-4,1) is 1, the

-coordinate of point B must also be 1.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The

-coordinate of all points in any given vertical line are identical. Therefore, the

-coordinate of all points on the line

is 2. That means that the midpoint of the segment AB must be (2,1).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The midpoint formula for

gives the

-coordinate of the midpoint given the

-coordinates of the endpoints:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But here we know the

-coordinate of one of the endpoints and the

-coordinate of the midpoint. So solve the formula for

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Substitute the known values and do the arithmetic.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Therefore B is the point (8, 1)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );