If the coordinates (x, y) of a point are given, one can plot in the Cartesian xy 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 xaxis 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 xcoordinate. Draw a perpendicular MN on the xaxis. Take a point P on this perpendicular such that MP is equal to the numerical value of the ycoordinate 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 coordinates (2, 3) as shown below.
(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 coordinates (2, 3) as shown below.
(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 coordinates (2, 3) as shown below.
(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 coordinates (2, 3) as shown below.
(v) (0, 3) is a point on the negative yaxis because xcoordinate = 0 and ycoordinate < 0. Following the steps 2 and 3 we plot the point P with coordinates (0, 3) as shown below.
These examples will help us to plot different coordinate points on Cartesian plane.
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