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Question
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)
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Solution
Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)
Let m1 be the slope of the line joining (9, 5) and (−1, 1) and m2 be the slope of the line joining (3, −5) and (8, −3).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{- 1 - 9} = \frac{- 4}{- 10} = \frac{2}{5} \text { and } m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{- 3 + 5}{8 - 3} = \frac{2}{5}\]
\[\text { Since, } m_1 = m_2\]
Therefore, the given lines are parallel.
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