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Question
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
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Solution
Let m1 be the slope of the line joining the points (2, −5) and (−2, 5) and m2 be the slope of the line joining the points (6, 3) and (1, 1).
\[\therefore m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 + 5}{- 2 - 2} = \frac{10}{- 4} = - \frac{5}{2}\] and \[m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{1 - 6} = \frac{- 2}{- 5} = \frac{2}{5}\]
\[\text { Now, } m_1 m_2 = - \frac{5}{2} \times \frac{2}{5} = - 1\]
\[\text { Since, } m_1 m_2 = - 1\]
Hence, the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
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