document.write( "Question 288074: If the vertices of the right angle triamgle ABC are A(-1,2) B(3,8) C(5,-2) use coordinate geometry to prove that point M,the midpoint of the hypotenuse is equidistant from all three vertices of the triangle. \n" ); document.write( "

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If the vertices of the right angle triamgle ABC are A(-1,2) B(3,8) C(5,-2) use coordinate geometry to prove that point M,the midpoint of the hypotenuse is equidistant from all three vertices of the triangle.
\n" ); document.write( "--------------------
\n" ); document.write( "BC is the hypotenuse
\n" ); document.write( "Mx = (3+5)/2 = 4
\n" ); document.write( "My = (8-2)/2 = 3
\n" ); document.write( "Midpoint M (4,3)
\n" ); document.write( "M is equidistant from B and C by definition.
\n" ); document.write( " $\"s%5E2+=+diffy%5E2+%2B+diffx%5E2\"$
\n" ); document.write( " $\"s%5E2+=+1+%2B+5%5E2+=+26\"$
\n" ); document.write( "-----------
\n" ); document.write( "Find the distance from M to A:
\n" ); document.write( " $\"s%5E2+=+5%5E2+%2B+1+=+26\"$
\n" ); document.write( "Same distance
\n" ); document.write( "QED \n" ); document.write( "

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