Page 1
CO-ORDINATE GEOMETRY
Coordinate geometry is the study of geometry with the help of algebra. The plane curves which would be
considered are : straight line, circle, parabola, ellipse and hyperbola.
The system of coordinates used here is cartesian system of coordinates, introduced by philosopher
Descartes. It is by far the most important system.
Page 2
CO-ORDINATE GEOMETRY
Coordinate geometry is the study of geometry with the help of algebra. The plane curves which would be
considered are : straight line, circle, parabola, ellipse and hyperbola.
The system of coordinates used here is cartesian system of coordinates, introduced by philosopher
Descartes. It is by far the most important system.
Cartesian System of Rectangular Co-ordinates
in a plane
To identify a point ?? in the two dimensional plane, we associate with it, an ordered pair of numbers, in
the following way:
Let ???? and ???? be two fixed perpendicular straight lines in the plane of the paper.
Page 3
CO-ORDINATE GEOMETRY
Coordinate geometry is the study of geometry with the help of algebra. The plane curves which would be
considered are : straight line, circle, parabola, ellipse and hyperbola.
The system of coordinates used here is cartesian system of coordinates, introduced by philosopher
Descartes. It is by far the most important system.
Cartesian System of Rectangular Co-ordinates
in a plane
To identify a point ?? in the two dimensional plane, we associate with it, an ordered pair of numbers, in
the following way:
Let ???? and ???? be two fixed perpendicular straight lines in the plane of the paper.
The line ???? is called, the axis of ?? ; the line ???? is called, the axis of ?? ; the two together are called the axes
of coordinates. The point ?? is called the origin (of reference) and ?????? is referred to as the Cartesian
system. We shall restrict ourselves to rectangular Cartesian system (where ???? and ???? are
perpendicular).
From any point ?? in the plane, draw lines ???? and ???? parallel to ?? and ?? axes respectively. The distance
???? = ?? is called as abscissa of ?? ; the distance ???? = ?? is called as ordinate of ?? ; the two together, i.e.
(?? , ?? ), are referred to as the coordinates of ?? .
Page 4
CO-ORDINATE GEOMETRY
Coordinate geometry is the study of geometry with the help of algebra. The plane curves which would be
considered are : straight line, circle, parabola, ellipse and hyperbola.
The system of coordinates used here is cartesian system of coordinates, introduced by philosopher
Descartes. It is by far the most important system.
Cartesian System of Rectangular Co-ordinates
in a plane
To identify a point ?? in the two dimensional plane, we associate with it, an ordered pair of numbers, in
the following way:
Let ???? and ???? be two fixed perpendicular straight lines in the plane of the paper.
The line ???? is called, the axis of ?? ; the line ???? is called, the axis of ?? ; the two together are called the axes
of coordinates. The point ?? is called the origin (of reference) and ?????? is referred to as the Cartesian
system. We shall restrict ourselves to rectangular Cartesian system (where ???? and ???? are
perpendicular).
From any point ?? in the plane, draw lines ???? and ???? parallel to ?? and ?? axes respectively. The distance
???? = ?? is called as abscissa of ?? ; the distance ???? = ?? is called as ordinate of ?? ; the two together, i.e.
(?? , ?? ), are referred to as the coordinates of ?? .
Distances measured along ???? are positive and those measured opposite to it are negative.
Distances measured in the direction of ???? are positive and those measured opposite to it
are negative.
?????? = 1st quadrant, Abscissa and ordinate both + ve
?? ?? '
?? = 2nd quadrant, Abscissa - ve and ordinate + ve
?? ?? '
?? '
= 3 rd quadrant, Abscissa - ve and ordinate - ve
???? ?? '
= 4th quadrant, Abscissa + ve and ordinate - ve
Page 5
CO-ORDINATE GEOMETRY
Coordinate geometry is the study of geometry with the help of algebra. The plane curves which would be
considered are : straight line, circle, parabola, ellipse and hyperbola.
The system of coordinates used here is cartesian system of coordinates, introduced by philosopher
Descartes. It is by far the most important system.
Cartesian System of Rectangular Co-ordinates
in a plane
To identify a point ?? in the two dimensional plane, we associate with it, an ordered pair of numbers, in
the following way:
Let ???? and ???? be two fixed perpendicular straight lines in the plane of the paper.
The line ???? is called, the axis of ?? ; the line ???? is called, the axis of ?? ; the two together are called the axes
of coordinates. The point ?? is called the origin (of reference) and ?????? is referred to as the Cartesian
system. We shall restrict ourselves to rectangular Cartesian system (where ???? and ???? are
perpendicular).
From any point ?? in the plane, draw lines ???? and ???? parallel to ?? and ?? axes respectively. The distance
???? = ?? is called as abscissa of ?? ; the distance ???? = ?? is called as ordinate of ?? ; the two together, i.e.
(?? , ?? ), are referred to as the coordinates of ?? .
Distances measured along ???? are positive and those measured opposite to it are negative.
Distances measured in the direction of ???? are positive and those measured opposite to it
are negative.
?????? = 1st quadrant, Abscissa and ordinate both + ve
?? ?? '
?? = 2nd quadrant, Abscissa - ve and ordinate + ve
?? ?? '
?? '
= 3 rd quadrant, Abscissa - ve and ordinate - ve
???? ?? '
= 4th quadrant, Abscissa + ve and ordinate - ve
Distance formula
Distance between points ?? (?? 1
, ?? 1
) and ?? (?? 2
, ?? 2
) i.e. length of line segment ???? is given by
???? = v(?? 1
- ?? 2
)
2
+ (?? 1
- ?? 2
)
2
Note: This formula is true for all points i.e. the points lying in any quadrant.
Distance of point ?? (?? 1
, ?? 1
) from origin is given by ???? = v?? 1
2
+ ?? 1
2
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