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Question
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (5, 6) and (2, 3); through (9, −2) and (6, −5)
Solution
Through (5, 6) and (2, 3); through (9, −2) and (6, −5)
Let m1 be the slope of the line joining (5, 6) and (2, 3) and m2 be the slope of the line joining (9, −2) and (6, −5).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 6}{2 - 5} = \frac{- 3}{- 3} = 1 \text { and } m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{- 5 + 2}{6 - 9} = \frac{- 3}{- 3} = 1\]
\[\text { Since }, m_1 = m_2\]
Therefore, the given lines are parallel.
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