Method to find co-ordinates of a point in a cartesian plane — lesson. Mathematics State Board, Class 9.

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Co-ordinates are ordered pairs used to represent the position of a point in the cartesian plane.

The terms

$(x, y)$ ,

$(-x, y)$ ,

$(-x,-y)$ ,

$(x,-y)$ are called co-ordinates which are used to locate the position of a point in the quadrants

$I$ ,

$II$ ,

$III$ and

$IV$ respectively in a cartesian plane.

$x$ -co-ordinate of a point:

The

$x$ -coordinate of a point is the perpendicular distance from the

$y$ -axis measured along the

$x$ -axis.

$y$ -co-ordinate of a point:

The

$y$ -coordinate of a point is the perpendicular distance from the

$x$ -axis measured along the

$y$ -axis.

1. The perpendicular distance of the point

$L$ from the

$y$ -axis measured along the positive direction of the

$y$ -axis is

$LX=4$ units and the perpendicular distance of the point

$L$ from the

$x$ -axis measured along the positive direction of the

$x$ -axis

$OL=3$ units.

Point

$L$ lies at the first quadrant in the above graph; hence its co-ordinates will be represented as

$(x, y)$ , where

$x=3$ and

$y=4$ is the co-ordinate of

$L$ in cartesian plane is represented as

$(3,4)$ .

2. The perpendicular distance of the point

$M$ from the

$y$ -axis measured along the positive direction of the

$y$ -axis is

$MX'=2$ units and the perpendicular distance of the point

$M$ from the

$x$ -axis measured along the negative direction of the

$x$ -axis

$OM=2$ units.

Point

$M$ lies at the second quadrant in the above graph; hence its co-ordinates will be represented as

$(-x, y)$ , where

$x=4$ and

$y=2$ is the co-ordinate of

$M$ in cartesian plane is represented

$(-4,2)$ .

3. The perpendicular distance of the point

$N$ from the

$y$ -axis measured along the negative direction of the

$y$ -axis is

$NX'=3$ units and the perpendicular distance of the point

$N$ from the

$x$ -axis measured along the negative direction of the

$x$ -axis

$OX'=2$ units.

Point

$N$ lies at the third quadrant in the above graph; hence its co-ordinates will be represented as

$(-x, -y)$ , where

$x=2$ and

$y=3$ is the co-ordinate of

$L$ in cartesian plane is represented as

$(-2,-3)$ .

4. The perpendicular distance of the point

$Q$ from the

$y$ -axis measured along the negative direction of the

$y$ -axis is

$QX=3$ units and the perpendicular distance of the point

$Q$ from the

$x$ -axis measured along the positive direction of the

$x$ -axis

$OX = 1$ unit.

Point

$Q$ lies at the fourth quadrant in the above graph; hence its co-ordinates will be represented as (x, -y), where

$x=1$ and

$y=3$ is the co-ordinate of

$L$ in cartesian plane is represented as

$(1,-3)$ .

Important!

Measure the positive coordinate value along the positive direction of the axis and the negative coordinate value along the negative direction of the axis.

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4. Method to find co-ordinates of a point in a cartesian plane

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