Distance from a point to a line: Difference between revisions

Revision as of 20:40, 16 May 2025

Revision as of 01:36, 21 June 2025

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'''Horizontal and vertical lines'''

In the general equation of a line, ''ax'' + ''by'' + ''c'' = 0, ''a'' and ''b'' cannot both be zero unless ''c'' is also zero, in which case the equation does not define a line. If ''a'' = 0 and ''b'' {{math|≠}} 0, the line is horizontal and has equation ''y'' = -−''c''/''b''. The distance from (''x''₀, ''y''₀) to this line is measured along a vertical line segment of length |''y''₀ -− (-−''c''/''b'')| = |''by''₀ + ''c''| / |''b''| in accordance with the formula. Similarly, for vertical lines (''b'' = 0) the distance between the same point and the line is |''ax''₀ + ''c''| / |''a''|, as measured along a horizontal line segment.

===Line defined by two points===