Where Do Two Perpendicular Lines Intersect?


Quick Answer

In Euclidean geometry, two perpendicular lines intersect at a single point called the intersection. If the two lines are y = ax + b and y = cx + d, then their intersection has x coordinate (d-b)/(a-c) and y coordinate [a(d-b)/(a-c) + b].

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Full Answer

Outside of Euclidean geometry, perpendicular lines may intersect at multiple points, but they always intersect at least one point. In spherical geometry, which is the geometry concerning the surface of a sphere, perpendicular lines intersect at two points. These points are directly across from each other and called antipodes. An example is the north and south poles of a sphere.

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