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Question
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)
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Solution
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5).
Let m1 be the slope of the line joining (6, 3) and (1, 1) and m2 be the slope of the line joining (−2, 5) and (2, −5).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{1 - 6} = \frac{- 2}{- 5} = \frac{2}{5} \text { and } m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{- 5 - 5}{2 + 2} = \frac{- 10}{4} = \frac{- 5}{2}\]
\[\text { Now,} m_1 m_2 = \frac{2}{5} \times \frac{- 5}{2} = - 1\]
\[\text { Since, } m_1 m_2 = - 1\]
Therefore, the given lines are perpendicular.
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