91
L10
Rectangular Coordinates; Graphs of Equations
The
Rectangular Coordinate System
is formed by the
x
−
axis and
y
−
axis.
A plane with the
rectangular
coordinate system
is called the
coordinate plane
or
xy

plane
.
This plane has four quadrants:
For each point
P
in the
xy

plane
, there is a
corresponding ordered pair (
,
)
x y
, where
x
and
y
are
called coordinates of
P
, and we write
( ,
)
P
x y
=
.
Example
: Determine the quadrant(s) in which (
,
)
x y
is
located if
0
x
<
and
0
y
<
2
x
>
and
3
y
=
92
Distance Formula
The distance between two points
1
1
1
(
,
)
P
x
y
=
and
2
2
2
(
,
)
P
x
y
=
, denoted by
1
2
(
,
)
d P P
, is
2
2
1
2
2
1
2
1
(
,
)
(
)
(
)
d P P
x
x
y
y
=
−
+
−
.
Note
:
1)
1
2
(
,
)
0
d P P
≥
2)
1
2
(
,
)
0
d P P
=
if and only if
1
2
P
P
=
3)
1
2
2
1
(
,
)
(
,
)
d P P
d P P
=
Midpoint
A point
M
on the line segment with endpoints
1
P
and
2
P
is called the
midpoint
if
1
2
(
,
)
(
,
)
d P M
d M P
=
.
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