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suleka
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.
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
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