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Formule e argomenti di matematica, fisica e scienze
Albert Einstein: ... la nostra conoscenza, se paragonata alla realta' e' primitiva e infantile. Eppure e' il bene piu' grande che possediamo.
... all our science, measured against reality, is primitive and childlike-and yet it is the most precious thing we have.


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Mathematics : Plane Analytical Geometry

Straight line

Theorem 1:
Any equation of the first degree in two variables (x, y), on a two dimensional plane, represents a straight line.

Theorem 2:
Any straight line on a given coordinate plane, can be described by an equation of the first degree in two variables (x, y) (*).

(*) The meaning is not ONE EQUATION ! We can have infinite equations changing k, (k ≠ 0) in kax + kby + kc = 0 (general equation of a straight line).


Symbols:
(SI)=Slope Y-Intercept equation, (GE)=General equation, (Sl)=Slope


_______ EQUATION AND SLOPE


Straight line equation and slope


___ Slope (given two points (P1, P2))

Slope , given p1 and p2



_______ SOME SPECIAL STRAIGHT LINES


___ Line passing through origin

Equation of line passing through origin

___ Equation of the Bisector of I and III quadrant

Bisector of I and III quadrant

___ Equation of the Bisector of II and IV quadrant

Bisector of II and IV quadrant

___ Line parallel to x-axis (1), y-axis (2)

Line parallel to x/y axis

___ Equation of x-axis (1), y-axis (2)

Equation of x-axis and y-axis

___ Line passing through one point: P(x0; y0)

Line through one point

___ Line passing through two points: P0(x0; y0), P1(x1; y1)

Line through two points


_______ CONDITION FOR TWO LINES TO BE PARALLEL


Parallel lines


_______ CONDITION FOR TWO LINES TO BE PERPENDICULAR


Perpendicular lines'


_______ FAMILY OF STRAIGHT LINE


___ PARALLEL FAMILY (k=changes; m=costant)
Family of straight lines




_______ DISTANCE FROM A POINT (P) TO A LINE (r)


Point to line distance

_______ ANGLE (α) BETWEEN TWO LINES


Angle between two lines


_______ BISECTORS OF THE ANGLES BETWEEN TWO LINES


Angle between two lines, bisectors

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