This document provides information about coordinate geometry and the Cartesian plane. It explains that coordinate geometry represents the position of objects in a plane using two perpendicular lines, known as axes. The system developed by René Descartes specifies each point using a pair of numerical coordinates representing the distance from the point to the two fixed axes. The axes divide the plane into four quadrants. Horizontal and vertical lines are designated relative to the axes and do not intersect each other.

1. MATHS HOLIDAY HOMEWORK
MADE BY
AMIT SINGH
CO-ORDINATEGEOMETRY

2. CO-ORDINATE GEOMETRY
 The position of any object lying on a plane can be represented with
the help of 2 perpendicular lines. This simple idea has far reaching
consequences, and has given rise to a very important branch of
Mathematics known as ‘Coordinate Geometry’. This study was
initially developed by the French philosopher and mathematician
Rene Descartes. In honor of Descartes, the system used for describing
the position of a point in a plane is also known as Cartesian Plane.

3. CARTESIAN PLANE

4. CARTESIAN PLANE
 A Cartesian coordinate system is a coordinate system that specifies
each point uniquely in a plane by a pair of numerical coordinates,
which are the signed distances from the point to two
fixed perpendicular directed lines, measured in the same unit of
length. Each reference line is called a coordinate axis or just axis of
the system, and the point where they meet is its origin, usually at
ordered pair (0, 0). The coordinates can also be defined as the
positions of the perpendicular projections of the point onto the two
axes, expressed as signed distances from the origin.

5.  The axes of a two-dimensional Cartesian system divide the
plane into four infinite regions, called quadrants, each
bounded by two half-axes. These are often numbered from
1st to 4th and denoted by Roman numerals: I (where the
signs of the two coordinates are I (+,+), II (−,+), III (−,−),
and IV (+,−). When the axes are drawn according to the
mathematical custom, the numbering goes counter-
clockwise starting from the upper right ("northeast")
quadrant.
CARTESIAN PLANE

6. To say that a line is horizontal or vertical, an initial designation has to be made.
One can start off by designating the vertical direction, usually labeled the Y
direction. The horizontal direction, usually labeled the X direction, is then
automatically determined. Or, one can do it the other way around, i.e.,
nominate the-axis, in which case the y-axis is then automatically determined.
There is no special reason to choose the horizontal over the vertical as the
initial designation: the two directions are on par in this respect.
The following hold in the two-dimensional case:
a) Through any point P in the plane, there is one and only one vertical line within
the plane and one and only one horizontal line within the plane. This
symmetry breaks down as one moves to the three-dimensional case.
b) A vertical line is any line parallel to the vertical direction. A horizontal line is
any line normal to a vertical line.
c) Horizontal and vertical lines do not cross each other.
CARTESIAN PLANE