Straight line
General equation of straight
line. Normal vector.
Equation of straight line with
slope.
Equation of straight line in
segments on axes.
Equation of straight line going
through two different points.
Parametric equation of straight
line.
Parallelism condition of straight
lines.
Perpendicularity condition of
straight lines.
Distance between two points.
Distance from point to straight
line.
Distance between parallel
straight lines.
Angle between straight lines.
A general equation of straight
line:
Àõ + Âó + Ñ =
0 ,
where
À
and Â
aren't equal to zero simultaneously.
Coefficients
À
and Â
are coordinates of normal vector of the
straight line
(
i.e.
vector, perpendicular to the
straight line
). At À
=
0 straight line is
parallel to the axis ÎÕ
, at
Â
=
0 straight line is
parallel to the axis ÎY
.
At
Â
0
we
receive an equation of straight line with a slope:
An equation of the straight line,
going through the point (
õ_{0
},
ó_{ 0}
) and not parallel to
the axis OY :
ó
– ó_{
0 }= m ( x
– õ_{0}
) ,
where m
is
a slope,
equal to tangent of an angle between the straight line and the positive
direction of the axis
ÎÕ
.
At
À
0,
Â
0 and
Ñ
0
we
receive an equation of straight line in segments on axes:
where a = – C / A,
b = – C / B. This line goes through the points (
a,
0
) and (
0, b
), i.e. it cuts off
segments a and b long on the coordinate axes.
An equation of straight line
going through two different points
( õ_{1},
ó_{ 1}
) and ( õ_{2},
ó_{ 2
}):
A parametric equation
of straight line,
going through a point
( õ_{0
},
ó_{
0}
) and parallel to a
direction vector (
a,
b
) of a straight line
:
A
parallelism condition of straight lines:
1) for lines Àõ+ Âó+
Ñ = 0 and Dõ+
Eó+
F = 0 : AE –
BD = 0 ,
2) for lines
ó
= m
x+ k
and ó
= p
x+ q
: m
=
p
.
A perpendicularity
condition of straight lines:
1) for lines
Àõ+ Âó+
Ñ = 0 and Dõ+
Eó+
F = 0 : AD +
BE = 0 ,
2) for lines
ó = m
x+ k
and
ó
= p
x+ q
: m
p
=
– 1 .
A
distance between two points
(
x_{1}
,
y_{
1}
)_{
}
and
(
x_{2}
,
y_{2}
) :
A distance from a point
(
õ_{0
},
ó_{
0}
) to a
straight line Àõ+
Âó+
Ñ
= 0 :
A distance between
parallel straight lines
Àõ+
Âó+
Ñ
=
0
and
Aõ+
Bó+
F
=
0 :
An angle
a
between straight lines:
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