Loney, S. L. (Sidney Luxton), 1860-1939 · London, Macmillan and co. · leaf 66
in-^ : 711^ is positive. In this case, by (3) the two quantities Ax^ + By^ + Cand Ax^ + By^ + C have opposite signs. The two points (a?i, y^ and {x^^ y^) therefore lie on the op- LENGTHS OF PEKPENDICULARS. 51 posite (or the same) sides of the straight line Ax + By + (7 = 0according as the… … (i) Let the equation of the straight line be £CCOSa+ 2/sin a —p = 0 (1), so that, if p be the perpendicular on it, we haveON^p and lXON=^o.. Let the given point F be {x ^ y). Through P draw PR parallel to the given line to meetOiV produced in R and draw PQ the required perpendicular.If OR be 2^i…
Coordinates · Geometry, Analytic
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