document.write( "Question 849870: Find the distance from (6,-3)to the line defined by y= 2x-5. Express as a radical or a number rounded to the nearest hundreth \n" ); document.write( "

Algebra.Com's Answer #511795 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "They did it the long way.  \r\n" );
document.write( "\r\n" );
document.write( "The formula for the distance from a point to a line is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where the equation of the line is Ax+By+C=0 and the point is (x₁,y₁)\r\n" );
document.write( "\r\n" );
document.write( "The point is (x₁,y₁) = (6,-3)\r\n" );
document.write( "The line's equation is y=2x-5. we must get that in the form\r\n" );
document.write( "Ax+By+C=0\r\n" );
document.write( "\r\n" );
document.write( "      y=2x-5.  We subtract the entire right side from both sides\r\n" );
document.write( " \r\n" );
document.write( "-2x+y+5=0\r\n" );
document.write( "\r\n" );
document.write( "A=-2, B=1, C=5, (x₁,y₁) = (6,-3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can rationalize the denominator by multiplying by .\r\n" );
document.write( "\r\n" );
document.write( ".\r\n" );
document.write( "\r\n" );
document.write( "That's about 4.47, so let's draw the graph as a check:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That green line looks like it's about 4.47 units in length.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );