3.
A system of geometry where the position of points on the plane is
described using an ordered pair of numbers.
The method of describing the location of points in this way was
proposed by the French mathematician René Descartes .
He proposed further that curves and lines could be described by
equations using this technique, thus being the first to link algebra
and geometry.
In honor of his work, the coordinates of a point are often referred to
as its Cartesian coordinates, and the coordinate plane as the
Cartesian Coordinate Plane. Coordinate Geometry
What is Coordinate Geometry?
4.
A Cartesian plane (named after French mathematician Rene
Descartes, who formalized its use in mathematics) is defined by two
perpendicular number lines: the x-axis, which is horizontal, and the
y-axis, which is vertical. Using these axes, we can describe any point
in the plane using an ordered pair of numbers. The
number plane or Cartesian plane is like two number lines that cross
at zero; one of them is horizontal and the other is vertical.
The Cartesian coordinate system is used to plot points.word
Cartesian emphaises logical analysis and its mechanistic
interpretation of physical nature. Etymology
What is Cartesian Plane?
5.
A coordinate plane is a two dimencinal plane formed
by the intersection of a vertical line called y-axis and
a horizontal line called x-axis. These are
perpendicular lines that intersect each other at zero,
and this point is called the origin. The axes cut the
coordinate plane into four equal sections, and each
section is known as quadrant.
What is Quadrant?
6. COORDINATE
PLANE
•The two-dimensional plane is called
the Cartesian plane, or the
coordinate plane and the axes are
called the coordinate axes or x-axis
and y-axis.
•The given plane has four equal
divisions by origin called
quadrants. Quadrant 1, Quadrant 2,
Quadrant 3 and Quadrant 4 show
the division of the quadrant plane.
•The horizontal line towards the
right of the origin (denoted by O) is
positive x-axis.
•The horizontal line towards the left
of the origin is negative x-axis.
•The vertical line above the origin is
positive y-axis.
•The vertical line below the origin is
negative y-axis.
•The two-dimensional plane is called the
Cartesian plane, or the coordinate plane and
the axes are called the coordinate axes or x-
axis and y-axis.
•The given plane has four equal divisions by
origin called quadrants. Quadrant 1,
Quadrant 2, Quadrant 3 and Quadrant 4
show the division of the quadrant plane.
•The horizontal line towards the right of the
origin (denoted by O) is positive x-axis.
•The horizontal line towards the left of the
origin is negative x-axis.
•The vertical line above the origin is positive
y-axis.
•The vertical line below the origin is negative
y-axis.
7.
To locate the position of a point on a plane,we require a
pair of coordinate axes.
The distance of a point from the y-axis is called its x-
coordinate, OR abscissa.
The distance of a point from the x-axis is called its y-
coordinate, OR ordinate.
The coordinates of a point on the x-axis are of the form (x,
0) and of a point on the y-axis are of the form (0, y).
SOME BASIC POINTS
8.
The x-coordinate or abscissa of a point is its perpendicular
distance from the y-axis measured along the x-axis.
The y-coordinate or ordinate of a point is its perpendicular
distance from the x-axis measured along the y-axis.
In stating the coordinates of a point in the coordinate
plane, the x-coordinate comes first, and then comes the y-
coordinate. We place the coordinates in brackets as (x, y).
The given conventions are followed to
locate the coordinates of a point:
9. To plot the ordered
pair (1, 3) in the
coordinate plane:
First, plot the number 1 on the x-
coordinate as it comes first in the
ordered pair.
Since it is a positive number, it
should move 1 unit from the
origin to the right.
Next, plot the number 3 on the y-
axis. As it is a positive number,
so it would move 3 units up on
the y-axis.
The graphical representation of
the ordered pair (1, 3) is shown
in the figure.
10. Formula of Coordinate Geometry
If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y
11.
R.D. Khosla . D.A .V. Model . Sr
.Sec School, Batala
Submitted By :- Ramanpreet Kaur
Class :- 9th ‘A’
Roll No. :- 26
