document.write( "Question 181501: Please help, I've been stuck on this question all day.\r
\n" ); document.write( "\n" ); document.write( "Decide whether or not the points are the vertices of a right triangle.\r
\n" ); document.write( "\n" ); document.write( "(-9,-4), (-5,-4), )-5,1) \n" ); document.write( "

Algebra.Com's Answer #136112 by Mathtut(3670) $\"\"$ $\"About$

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you only need prove that the line from (-5,1) to (-5,-4) lets call this line a is perpendicular to the line from (-9,-4) to (-5,-4)lets call this line b
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\n" ); document.write( "In order to do this we need to find the slopes. remember perpendicular lines have slopes that are negative recipricals of each other
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\n" ); document.write( "problem here is one line is vertical so undefined slope. the other is horizontal line which is slope zero. that by itself really proves lines are perpendicular . but teacher probably wants further proof
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\n" ); document.write( "so we will use distances
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\n" ); document.write( "we know the distance of line a is 5 and we know the distance of line b is 4
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\n" ); document.write( "so $\"4%5E2%2B5%5E2=c%5E2\"$ so c= $\"sqrt%2841%29\"$ meaning that for this to be a right triangle the hypothenuse has to be $\"sqrt%2841%29\"$
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\n" ); document.write( "lets use the distance formula for line c which is from point (-5,1) to (-9,-4)
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\n" ); document.write( " $\"D=sqrt%28%28-5-%28-9%29%29%5E2%2B%281-%28-4%29%29=4%5E2%2B5%5E2=41%29\"$
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\n" ); document.write( "so $\"D=sqrt%2841%29\"$
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\n" ); document.write( "using pathagorean theorem and the distance formula we have proved this is a right triangle \n" ); document.write( "

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