Question 181501
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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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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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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so we will use distances
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we know the distance of line a is 5 and we know the distance of line b is 4
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so {{{4^2+5^2=c^2}}} so c={{{sqrt(41)}}} meaning that for this to be a right triangle the hypothenuse has to be {{{sqrt(41)}}}
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lets use the distance formula for line c which is from point (-5,1) to (-9,-4)
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{{{D=sqrt((-5-(-9))^2+(1-(-4))=4^2+5^2=41)}}}
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so {{{D=sqrt(41)}}}
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using pathagorean theorem and the distance formula we have proved this is a right triangle