document.write( "Question 1020439: Im really stuck!
\n" ); document.write( "ABC is an isosceles triangle. The coordinates of A and B are (5,6) and (0,-4) respectively. Given that the gradient of BC is 3/4 and D is the midpoint of BC find:\r
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\n" ); document.write( "\n" ); document.write( "how do i find equation of AD only with 2 points? \n" ); document.write( "
Algebra.Com's Answer #636333 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let the unknown point D be D(h,k).\r\n" );
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document.write( "We can find the equation of AD because we are given\r\n" );
document.write( "its gradient 3/4 and its y-intercept (0,-4)\r\n" );
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document.write( "\"matrix%281%2C5%2Cy%2C%22%22=%22%22%2Cexpr%283%2F4%29x%2C%22%22%2B%22%22%2C%28-4%29%29\"\r\n" );
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document.write( "\"matrix%281%2C5%2Cy%2C%22%22=%22%22%2Cexpr%283%2F4%29x%2C%22%22-%22%22%2C4%29\"\r\n" );
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document.write( "That's the equation of AD.\r\n" );
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document.write( "Next we find the length of AB using the distance formula:\r\n" );
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document.write( "\"d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "\"AB=sqrt%28%28%286%29-%28-4%29%5E%22%22%29%5E2%2B%28%285%29-%280%29%29%5E2%29\"\r\n" );
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document.write( "\"AB=sqrt%28%286%2B4%29%5E2%2B%285-0%29%5E2%29\"\r\n" );
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document.write( "\"AB=sqrt%28%2810%29%5E2%2B%285%29%5E2%29\"\r\n" );
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document.write( "\"AB=sqrt%28100%2B25%29\"\r\n" );
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document.write( "\"AB=sqrt%28125%29\"\r\n" );
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document.write( "\"AB=sqrt%2825%2A5%29\"\r\n" );
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document.write( "\"AB=5sqrt%285%29\"\r\n" );
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document.write( "Since triangle ABC is isosceles, we know that\r\n" );
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document.write( "\"BC=AB=5sqrt%285%29\"\r\n" );
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document.write( "And since D is the midpoint of BC, then AD is\r\n" );
document.write( "one-half of BC, so\r\n" );
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document.write( "\"BD=5sqrt%285%29%2F2\"\r\n" );
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document.write( "We use the distance formula and set the length \r\n" );
document.write( "of BD equal to this:\r\n" );
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document.write( "\"d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "Square both sides of the equation:\r\n" );
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document.write( "\"d%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2\"\r\n" );
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document.write( "So we have this equation, setting \"5sqrt%285%29%2F2\" \r\n" );
document.write( "equal to the distance from B(0,-4) to D(h,k):\r\n" );
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document.write( "\"%2825%2A5%29%2F4=%28h%29%5E2%2B%28k%2B4%29%5E2\"\r\n" );
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document.write( "\"125%2F4=h%5E2%2B%28k%2B4%29%5E2\"\r\n" );
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document.write( "Multiply through by 4 to clear the fraction:\r\n" );
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document.write( "\"125=4h%5E2%2B4%28k%2B4%29%5E2\"\r\n" );
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document.write( "Since we know that D(h,k) is a point on line AD,\r\n" );
document.write( "whose equation is \r\n" );
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document.write( "\"matrix%281%2C5%2Cy%2C%22%22=%22%22%2Cexpr%283%2F4%29x%2C%22%22-%22%22%2C4%29\"\r\n" );
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document.write( "So D(h,k) it must satisfy that equation: \r\n" );
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document.write( "\"k=expr%283%2F4%29h-4\".\r\n" );
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document.write( "So we substitute that for k in\r\n" );
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document.write( "\"125=4h%5E2%2B4%28k%2B4%29%5E2\"\r\n" );
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document.write( "\"125=4h%5E2%2B4%28expr%283%2F4%29h-4%2B4%29%5E2\"\r\n" );
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document.write( "\"125=4h%5E2%2B4%28expr%283%2F4%29h%29%5E2\"\r\n" );
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document.write( "\"125=4h%5E2%2B4%2Aexpr%289%2F16%29h%5E2\"\r\n" );
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document.write( "\"125=4h%5E2%2Bexpr%289%2F4%29h%5E2\"\r\n" );
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document.write( "Multiply through by 4\r\n" );
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document.write( "\"500=16h%5E2%2B9h%5E2%29\"\r\n" );
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document.write( "\"500=25h%5E2\"\r\n" );
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document.write( "\"20=h%5E2\"\r\n" );
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document.write( "\"sqrt%2820%29=h\"\r\n" );
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document.write( "\"sqrt%284%2A5%29=h\"\r\n" );
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document.write( "\"2sqrt%285%29=h\"\r\n" );
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document.write( "\"k=expr%283%2F4%29h-4\"\r\n" );
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document.write( "\"k=expr%283%2F4%29%282sqrt%285%29%29-4\"\r\n" );
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document.write( "\"k=expr%283%2F4%29%282sqrt%285%29%29-4\"\r\n" );
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document.write( "\"k=expr%283%2F2%29sqrt%285%29-4\"\r\n" );
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document.write( "\"k=%283sqrt%285%29-8%29%2F2\"\r\n" );
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document.write( "So the coordinates of point D is\r\n" );
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document.write( "\"%28matrix%281%2C3%2C2sqrt%285%29%2C%22%2C%22%2C%283sqrt%285%29-8%29%2F2%29%29\"\r\n" );
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document.write( "Edwin
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