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Question

# Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. The family of orthogonal trajectories for a family of parallel lines is another family of parallel lines.

Solution

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The best way to show that this is true is by a picture, like the one on the left. But if you have lines that all have the same slope, which is the definition of a parallel line, say the slope for these lines is m. The perpendicular lines would all have the same slope $\dfrac{-1}{m}$ as well because the slopes of the original family were the same.

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