document.write( "Question 1060048: For the Initial point of (1,11) and the Terminal point of (9,3), how would you find the component and magnitude? \n" ); document.write( "

Algebra.Com's Answer #675109 by jim_thompson5910(35256) $\"\"$ $\"About$

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Subtract the x coordinates (terminal - initial) to get
\n" ); document.write( "9-1 = 8\r
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\n" ); document.write( "\n" ); document.write( "Do the same for the y coordinates
\n" ); document.write( "3-11 = -8\r
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\n" ); document.write( "\n" ); document.write( "So the component form of this vector is < 8, -8 >\r
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\n" ); document.write( "\n" ); document.write( "Let's find the magnitude now. We'll use this formula
\n" ); document.write( "d = sqrt(a^2 + b^2)
\n" ); document.write( "where \"sqrt\" stands for \"square root\"\r
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\n" ); document.write( "\n" ); document.write( "In this case, a = 8 and b = -8, so\r
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\n" ); document.write( "\n" ); document.write( "d = sqrt(a^2 + b^2)
\n" ); document.write( "d = sqrt(8^2 + (-8)^2)
\n" ); document.write( "d = sqrt(128)
\n" ); document.write( "d = sqrt(64*2)
\n" ); document.write( "d = sqrt(64)*sqrt(2)
\n" ); document.write( "d = 8*sqrt(2) exact form
\n" ); document.write( "d = 11.3137084989848 approximate form\r
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\n" ); document.write( "\n" ); document.write( "The exact magnitude is 8*sqrt(2)\r
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\n" ); document.write( "\n" ); document.write( "while the approximate magnitude is 11.3137084989848
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