document.write( "Question 393235: Find the shortest distance from the point (-2,7) to the line 5x – 2y – 34 = 0. Round your answer to the nearest tenth. \n" ); document.write( "

Algebra.Com's Answer #279123 by Alan3354(69443) $\"\"$ $\"About$

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Find the shortest distance from the point (-2,7) to the line 5x – 2y – 34 = 0. Round your answer to the nearest tenth.
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\n" ); document.write( "First, find the eqn of the line perpendicular to the given line thru the point.
\n" ); document.write( "Slope of the given line = 5/2
\n" ); document.write( "Slope m of the perpendicular line = -2/5
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\n" ); document.write( "y-7 = (-2/5)(x+2)
\n" ); document.write( "2x + 5y = 31 is the line perpendicular thru (-2,7)
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\n" ); document.write( "Solve for the intersection of the lines:
\n" ); document.write( "5x – 2y = 34
\n" ); document.write( "2x + 5y = 31
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\n" ); document.write( "(8,3) is the intersection
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\n" ); document.write( "Find the distance from (-2,7) to (8,3)
\n" ); document.write( " $\"d+=+sqrt%28diffy%5E2+%2B+diffx%5E2%29+=+sqrt%284%5E2+%2B+10%5E2%29\"$
\n" ); document.write( "d =~ 10.8 units
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\n" ); document.write( "There might be a better way to do these, I'll check into it.\r
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