document.write( "Question 388362: Hi,
\n" ); document.write( "I need some help in this problem.
\n" ); document.write( "the vertices of a triangle are A(0,0) B(x1,0) C(x2,y2). M, N are the midpoints of AB,AC.
\n" ); document.write( "a) write the coordinates of M,N.
\n" ); document.write( "b) show that MN=1/2 BC\r
\n" ); document.write( "\n" ); document.write( "I got part a bur i didn't get b.\r
\n" ); document.write( "\n" ); document.write( "Thank you!!! \n" ); document.write( "

Algebra.Com's Answer #275169 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "There is a difficulty here with conflicting notation because the \r\n" );
document.write( "formulas you must use, which are:\r\n" );
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document.write( "The midpoint between (x₁, y₁) and (x₂, y₂) has coordinates:\r\n" );
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document.write( "(, ) \r\n" );
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document.write( "and\r\n" );
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document.write( "The distance d between (x₁, y₁) and (x₂, y₂) is given by:\r\n" );
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document.write( "already have x₁, x₂, y₁ and y₂ in them.  When such a situation of conflicting\r\n" );
document.write( "notation arises, we must either change the notation in the problem, or else\r\n" );
document.write( "change the notation in the formula. We will change the notation in the\r\n" );
document.write( "problem.  So, let's rewrite the problem as this instead:\r\n" );
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document.write( "The vertices of a triangle are A(0,0) B(p,0) C(q,r). \r\n" );
document.write( "M, N are the midpoints of AB,AC.\r\n" );
document.write( "a) write the coordinates of M,N.\r\n" );
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document.write( "Use the midpoint formula to find the coordinates of M:\r\n" );
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document.write( "M(, )\r\n" );
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document.write( "Substitute \r\n" );
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document.write( "(x₁, y₁) = (0,0) and (x₂, y₂) = (p,0)  \r\n" );
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document.write( "M(, )\r\n" );
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document.write( "M(, )\r\n" );
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document.write( "M(, 0)\r\n" );
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document.write( "Use the midpoint formula to find the coordinates of N:\r\n" );
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document.write( "N(, )\r\n" );
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document.write( "Substitute \r\n" );
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document.write( "(x₁, y₁) = (0,0) and (x₂, y₂) = (q,r)  \r\n" );
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document.write( "N(, )\r\n" );
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document.write( "N(, )\r\n" );
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document.write( "N(, )\r\n" );
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document.write( "b) show that MN = BC \r\n" );
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document.write( "Let's find MN and BC, using the distance formula.  Let's find BC first:\r\n" );
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document.write( "(x₁, y₁) = (p,0) and (x₂, y₂) = (q,r)\r\n" );
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document.write( "Now let's find MN:\r\n" );
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document.write( "(x₁, y₁) = (,0) and (x₂, y₂) = (,)\r\n" );
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document.write( "Write  as ,  as , and  as ,\r\n" );
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document.write( "Factor out  inside the first parentheses:\r\n" );
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document.write( "Remove the outer parentheses in both expression under the radical\r\n" );
document.write( "by squaring the two factors individually:\r\n" );
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document.write( "Write the  as \r\n" );
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document.write( "Factor  out under the radical:\r\n" );
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document.write( "Take indivisual square roots:\r\n" );
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document.write( "Write  as \r\n" );
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document.write( "Now we notice that the right side of that is  times the right side of\r\n" );
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document.write( "So we have proved that MN = BC\r\n" );
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document.write( "Edwin

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