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Question
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
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Solution
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Let m1 be the slope of the line joining (3, 15) and (16, 6) and m2 be the slope of the line joining (−5, 3) and (8, 2).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 15}{16 - 3} = \frac{- 9}{13} \text { and } m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{8 + 5} = \frac{- 1}{13}\]
\[\text { Now }, m_1 m_2 = \frac{- 9}{13} \times \frac{- 1}{13} = \frac{9}{169}\]
\[\text { Since, } m_1 m_2 \neq - 1 \text { and } m_1 \neq m_2\]
Therefore, the given lines are neither parallel nor perpendicular.
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