document.write( "Question 730942: Let P(-3,6) and Q(10,1) be two points in the coordinate plane \r
\n" ); document.write( "\n" ); document.write( "Find an equation of the circle that contains P and Q and whose center is the midpoint of the segment PQ
\n" ); document.write( "

Algebra.Com's Answer #446942 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
The standard equation of a circle with center C(\"h\",\"k\") and radius \"r\" is as follows:\r
\n" ); document.write( "\n" ); document.write( "\"%28x-h%29%5E2+%2B+%28y+-k%29%5E2+=+r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "so, we need to find \"h\",\"+k\", and \"r\"\r
\n" ); document.write( "\n" ); document.write( "since the circle that contains P and Q , the distance between them is equal to diameter of the circle:\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: Distance Formula

\n" ); document.write( "
\n" ); document.write( " The first point is (x1,y1). The second point is (x2,y2)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6)
\n" ); document.write( " So \"x%5B1%5D+=+-3\", \"y%5B1%5D+=+6\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Since the second point is (10, 1), we can also say (x2, y2) = (10, 1)
\n" ); document.write( " So \"x%5B2%5D+=+10\", \"y%5B2%5D+=+1\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Put this all together to get: \"x%5B1%5D+=+-3\", \"y%5B1%5D+=+6\", \"x%5B2%5D+=+10\", and \"y%5B2%5D+=+1\"
\n" ); document.write( "
\n" ); document.write( " --------------------------------------------------------------------------------------------
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Now use the distance formula to find the distance between the two points (-3, 6) and (10, 1)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"d+=+sqrt%28%28-3+-+10%29%5E2+%2B+%286+-+1%29%5E2%29\" Plug in \"x%5B1%5D+=+-3\", \"y%5B1%5D+=+6\", \"x%5B2%5D+=+10\", and \"y%5B2%5D+=+1\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"d+=+sqrt%28%28-13%29%5E2+%2B+%285%29%5E2%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"d+=+sqrt%28169+%2B+25%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"d+=+sqrt%28194%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"d+=+13.9283882771841\"
\n" ); document.write( "
\n" ); document.write( " ==========================================================
\n" ); document.write( "
\n" ); document.write( " Answer:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " The distance between the two points (-3, 6) and (10, 1) is exactly \"sqrt%28194%29\" units
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " The approximate distance between the two points is about 13.9283882771841 units
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So again,
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Exact Distance: \"sqrt%28194%29\" units
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Approximate Distance: \"13.9283882771841\" units
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, diameter \"d=13.9\"...=>...\"r=13.9%2F2\"...=>...\"r=6.95\"\r
\n" ); document.write( "\n" ); document.write( "now find midpoint:\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: Midpoint

\n" ); document.write( "
\n" ); document.write( " The first point is (x1,y1). The second point is (x2,y2)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6)
\n" ); document.write( " So \"x%5B1%5D+=+-3\", \"y%5B1%5D+=+6\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Since the second point is (10, 1), we can also say (x2, y2) = (10, 1)
\n" ); document.write( " So \"x%5B2%5D+=+10\", \"y%5B2%5D+=+1\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Put this all together to get: \"x%5B1%5D+=+-3\", \"y%5B1%5D+=+6\", \"x%5B2%5D+=+10\", and \"y%5B2%5D+=+1\"
\n" ); document.write( "
\n" ); document.write( " ----------------------------------------------------------------------------------------
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " X Coordinate of Midpoint = \"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " X Coordinate of Midpoint = \"%28-3%2B10%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " X Coordinate of Midpoint = \"7%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " X Coordinate of Midpoint = \"3.5\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So the x coordinate of the midpoint is 3.5
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " ----------------------------------------------------------------------------------------
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Y Coordinate of Midpoint = \"%28y%5B1%5D%2By%5B2%5D%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Y Coordinate of Midpoint = \"%286%2B1%29%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Y Coordinate of Midpoint = \"7%2F2\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Y Coordinate of Midpoint = \"3.5\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So the y coordinate of the midpoint is 3.5
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " ===============================================================================
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Summary:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " The midpoint of the segment joining the two points (-3, 6) and (10, 1) is (3.5, 3.5).
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So the answer is (3.5, 3.5)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "center is (\"3.5\", \"3.5\")=(\"h\",\"+k\")...so \"h=3.5\" and \"k=3.5\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x-h%29%5E2+%2B+%28y+-k%29%5E2+=+r%5E2\"...plug in \"h=3.5\",\"k=3.5\", and \"r=6.95\"\r
\n" ); document.write( "\n" ); document.write( "your equation is:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28x-3.5%29%5E2+%2B+%28y+-3.5%29%5E2+=+6.95%5E2\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );