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The line that is perpendicular to
\n" ); document.write( "y = 2x - 3 has a gradient of -1/2
\n" ); document.write( "For lines perpendicular to each other
\n" ); document.write( "their gradients multiply together to
\n" ); document.write( "give -1
\n" ); document.write( "(m1 x m2 = -1)
\n" ); document.write( "Using the formula y -b =m(x - a)
\n" ); document.write( "with m = -1/2 and coordinates (6, -1)
\n" ); document.write( "y - (-1) = -1/2(x - 6)
\n" ); document.write( " y + 1 = -1/2x + 3
\n" ); document.write( " y = -1/2x + 3 - 1
\n" ); document.write( " y = -1/2x + 2
\n" ); document.write( "OR 2y = -x + 4
\n" ); document.write( " To find where line 2y = -x + 4
\n" ); document.write( "and y = 2x - 3 meet, set out and
\n" ); document.write( "solve simultaneous equations:-\r
\n" ); document.write( "\n" ); document.write( " 2y + x = +4....1
\n" ); document.write( " y -2x = -3.....2
\n" ); document.write( "Multiply (1) by 2
\n" ); document.write( " 4y + 2x = 8
\n" ); document.write( " y - 2x = -3
\n" ); document.write( "Add
\n" ); document.write( " 5y = 5
\n" ); document.write( " y = 1
\n" ); document.write( "Substitute y = 1 into Eq. 2
\n" ); document.write( " y - 2x = - 3
\n" ); document.write( " 1 - 2x = - 3
\n" ); document.write( " - 2x = - 3 - 1
\n" ); document.write( " - 2x = -4
\n" ); document.write( " x = 2
\n" ); document.write( "So, this is the point where the lines meet.\r
\n" ); document.write( "\n" ); document.write( "Distance from (6, -1) and (1,2)
\n" ); document.write( "Square root((x2 - x1)^2 + (y2 - y1)^2)
\n" ); document.write( "Square root ( (1 - 6)^2 + (2 - (-1))^2)
\n" ); document.write( "Square root (5^2 + 3^2)
\n" ); document.write( " Square root(34)
\n" ); document.write( " = 5.8 units \n" ); document.write( "