document.write( "Question 315051: find all points having an x coordinate of 9, whose distance from the point (3,-2) is 10 \n" ); document.write( "
Algebra.Com's Answer #225363 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
find all points having an x coordinate of 9, whose distance from the point (3,-2) is 10
\n" ); document.write( "
\r\n" );
document.write( "All points which have x coordinate 9 are on the vertical\r\n" );
document.write( "green line below:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "we take a compass and open it up to a radius of 10 units.\r\n" );
document.write( "We put the sharp point of the compass on the point (3,-2) \r\n" );
document.write( "and we find that can swing two red arc to cut the green vertical\r\n" );
document.write( "line in two points, like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we draw 10-unit long blue lines from (3,-2) to the \r\n" );
document.write( "points where the arcs cut the green line:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Those two points look like they are (9,6)  and (9,-10), but\r\n" );
document.write( "looking and estimating is not good enough for mathematics.\r\n" );
document.write( "We must calculate them:\r\n" );
document.write( "\r\n" );
document.write( "Let's draw a black horizontal line segment from (3,-2) over to the\r\n" );
document.write( "green vertical line:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That line segment is 6 units long because it extends horizontally\r\n" );
document.write( "from the point (3,-2) over to (9,-2) and that is 6 units.  \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "If we look just at the top half, we have a right triangle, with\r\n" );
document.write( "hypotenuse 10 units and horizontal leg 6 units, like this.  Call the\r\n" );
document.write( "length of the green side of the right triangle h,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "By the Pythagorean theorem\r\n" );
document.write( "\r\n" );
document.write( "\"6%5E2+%2B+h%5E2+=+10%5E2\"\r\n" );
document.write( "\"36%2Bh%5E2=100\"\r\n" );
document.write( "\"h%5E2=100-36\"\r\n" );
document.write( "\"h%5E2=64\"\r\n" );
document.write( "\"h=sqrt%2864%29\"\r\n" );
document.write( "\"h=8\"\r\n" );
document.write( "\r\n" );
document.write( "So the upper vertex of that right triangle\r\n" );
document.write( "is 8 units above (9,-2) so it must be (9,6),\r\n" );
document.write( "just as we guessed just by looking.\r\n" );
document.write( "\r\n" );
document.write( "Putting back the lower right triangle, which is congruent to\r\n" );
document.write( "the upper one:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the lower vertex of that lower right triangle\r\n" );
document.write( "is 8 units below (9,-2) so it must be (9,-10),\r\n" );
document.write( "just as we guessed just by looking.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );