Plotting a Point in Cartesian plane

If the coordinates (x, y) of a point are given, one can plot in the Cartesian x-y plane by taking the following steps.

Step I: Observe the signs of the coordinates and determine the quadrant in which the point should be plotted.

Step II: Take a rectangular Cartesian frame of axes XOX’ and YOY’ cutting each other at right angles at O.

Step III: Take a point M on the x-axis on the side of the concerned quadrant such that the distance of the point M from the origin O equals the numerical value of the x-coordinate. Draw a perpendicular MN on the x-axis. Take a point P on this perpendicular such that MP is equal to the numerical value of the y-coordinate and P is in the concerned quadrant. Thus P is plotted according to its given coordinates.

Examples on plotting a point in Cartesian plane:

Plot the following points in Cartesian plane:

(i) (2, 3)

(ii) (2, -3)

(iii) (-2, -3)

(iv) (-2, 3)

(v) (2, 0)

(vi) (0, -3)

Solution:

(i) (2, 3) is a point in the first quadrant because 2 > 0, 3 > 0. Following the steps 2 and 3 we plot the point P with co-ordinates (2, 3) as shown below.

First Coordinate Point

 

(ii) (2, -3) is a point in the fourth quadrant because 2 > 0, -3 < 0. Following the steps 2 and 3 we plot the point P with co-ordinates (2, -3) as shown below.

Fourth Coordinate Point


(iii) (-2, -3) is a point in the third quadrant because -2 < 0, -3 < 0. Following the steps 2 and 3 we plot the point P with co-ordinates (-2, -3) as shown below.

Third Coordinate Point


(iv) (-2, 3) is a point in the second quadrant because -2 < 0, 3 > 0. Following the steps 2 and 3 we plot the point P with co-ordinates (-2, 3) as shown below.


(v) (0, -3) is a point on the negative y-axis because x-coordinate = 0 and y-coordinate < 0. Following the steps 2 and 3 we plot the point P with co-ordinates (0, -3) as shown below.

Point on Negative y-Coordinate

These examples will help us to plot different co-ordinate points on Cartesian plane.






9th Grade Math

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