# Coordinates of a Point in a Plane

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:

Coordinate Graph

Signs of Coordinates

Find the Coordinates of a Point

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