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When graphed, the first line has a slope defined by a rise of ( A ) and a run of ( B ), while the second line has a slope characterized by a rise of (-B) and a run of ( A ). The intersections of these lines, by virtue of their slopes being negative reciprocals, confirm their perpendicular nature.
The Geometry of Perpendicular Lines
In geometric terms, if we shift the axes around the origin, the essence of how angles and slopes interact does not change. Through manipulation, we can visualize that simply rotating the axes shows us that the relationship between the slopes remains intact, ensuring their perpendicular intersection.