How to determine the coordinates of a point in a plane?
\(\overrightarrow{XOX'}\) and \(\overrightarrow{YOY'}\) represent the co-ordinate axes. P be a point in the plane of the graph paper.
Draw \(\overline{PM}\) ┴ \(\overrightarrow{YOY'}\) and \(\overline{PN}\) ┴ \(\overrightarrow{XOX'}\).
Length of \(\overline{ON}\) is called the x- co-ordinate or abscissa of point P. Here \(\overline{ON}\) = 2 units.
Length of \(\overline{OM}\) is called the y-co-ordinate or ordinate of P. Here \(\overline{OM}\) = 4 units.
Thus, the co-ordinates of point P are (2, 4) which is called an ordered pair.
So, the positions of the coordinates of a point in a plane cannot be interchanged as (4, 2).
Remember, if the distance of P from y-axis is ‘a’ and units the distance of P from the x-axis is ‘b’ units then the co-ordinates of point P are (a, b) where a denotes the x-co-ordinate or abscissa and b denotes the y-co-ordinate or ordinate.
Thus, we can define abscissa as distance of P from y-axis and ordinate as the distance of P from x-axis.
Point on x-axis: If we take any point on x-axis, then the distance of this point from x-axis is zero i.e., y-co-ordinate of every point on x-axis is zero.
Therefore, the co-ordinates of a point on x-axis are of the form (x, 0)
Point on y-axis: If we take any point on y-axis, then the distance of this point from y-axis is zero i.e., x-co-ordinate of every point on y-axis is zero.
Therefore, the co-ordinates of a point on y-axis are of the form (0, y).
Related Concepts:
● Ordered pair of a Coordinate System
● Find the Coordinates of a Point
● Plot Points on Co-ordinate Graph
● Simultaneous Equations Graphically
● Graph of Perimeter vs. Length of the Side of a Square
● Graph of Area vs. Side of a Square
● Graph of Simple Interest vs. Number of Years
7th Grade Math Problems
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