document.write( "Question 389312: Hello, I can't seem to figure this out and was hoping someone could help.\r
\n" ); document.write( "\n" ); document.write( "Find the coordinates of point D on line BC such that AD is the shortest distance from A to BC for A(9,9, B(-1,-1), and C(-2,2).\r
\n" ); document.write( "\n" ); document.write( "Thanks. \n" ); document.write( "
Algebra.Com's Answer #275908 by robertb(5830)\"\" \"About 
You can put this solution on YOUR website!
The slope from the point B(-1,-1) to C (-2,2) is (2--1)/(-2--1) = 3/(-1) = -3. The equation of the line is y--1 = -3(x--1) ----->y+1 = -3(x+1) ----->y = -3x-3 - 1 -----> y = -3x-4.
\n" ); document.write( "Now the find the equation of the line perpendicular to the line y = -3x-4 and passing through A(9,9). The slope of that line must be 1/3 (the negative reciprocal of -3). Then the equation of the line is y - 9 = (x-9)/3.
\n" ); document.write( "----> 3y - 27 = x - 9 ----> 3y = x + 18.
\n" ); document.write( "We now have to solve the system
\n" ); document.write( " y = -3x-4
\n" ); document.write( " 3y = x + 18
\n" ); document.write( "Substitute the top equation into the bottom equation:
\n" ); document.write( "3(-3x-4) = x + 18;
\n" ); document.write( "-9x-12 = x + 18;
\n" ); document.write( "-30 = 10x;
\n" ); document.write( "x = -3.------>y = -3*-3 - 4 = 9-4 = 5.
\n" ); document.write( "Therefore segment AD is minimum for the point D(-3,5). \n" ); document.write( "
\n" );