Plane and solid analytic geometry; an elementary textbook (1904)
Ashton, Charles Hamilton, 1866-1936 · New York, C. Scribner's Sons · leaf 51
, or a singlepoint and the direction of the line. If either of these setsof conditions is given, the line is fully determined, and weshould be able to find the algebraic relation which must besatisfied by every point on it. 23. Line through two points. — Let the line pass throughthe two points Pv… … P1KP2 we haveLP KP 2.. Fig. 27. PXL PXK But LP = y- yxPXL = x — xvKP2 = y2- yvP1K=x2 -xv 34 Ch. IV. §23] THE STRAIGHT LINE 35 Substituting these values, we have y -V\ = Vi-y\t 1-5-1 This is then the algebraic relation between the coordi-nates x and y of any point on the line and the constantsxv yv…
Geometry, Analytic
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