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Question
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
Solution
Let m1 be the slope of the line joining the points (2, −3) and (−5, 1) and m2 be the slope of the line joining the points (7, −1) and (0, 3).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 + 3}{- 5 - 2} = - \frac{4}{7}\] and \[m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 + 1}{0 - 7} = - \frac{4}{7}\]
Since, m1 = m2
Hence, the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
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