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Is the line through points P(–8, –10) and Q(–5, –12) perpendicular to the line through points R(9, –6) and S(17, –5)? Explain.

Mathematics
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no, because when the lines intersect they should intersect at 90 degree angles. They do not.
\[\tan \theta=\frac{m_1-m_2}{1+m_1m_2}\] \[m=\frac{y_2-y_1}{x_2-x_1}\] \[m_1=\frac{-5-(-6)}{17-9}=1/8\] \[m_2=\frac{-12-(-10)}{-5-(-8)}=-2/3\] \[\tan \theta=\frac{-2/3-1/8}{1+(-2/3)*1/8)}=19/22\] \[\theta=\tan^{-1} (19/22)\] \[\theta=40.8\]
talk about taking it further than necessary

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the shortest way is that, if they are perpendicular then multiply of their slop must be -1 if \[ \theta=90 \] then this must \[m_1*m_2=-1\] and we know that \[m_1*m_2=-1/12\] hence \[\theta\] cannot equal to 90

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