Question

What is the ordinate of any point on the x-axis?

Answer 1

Hint: First of all, take two points P and Q that are lying on the x-axis and x-coordinates \[{{x}_{1}}\] and \[{{x}_{2}}\] respectively. Since the points P and Q are next to the origin, the y-coordinates of points P and Q are equal to the y-coordinate of origin. We also know that the ordinate of a point is it’s y-coordinate. Now, conclude the answer.

Complete step by step answer:
According to the question, we are asked to find the ordinate of a point lying on the x-axis.
First of all, we need to know about ordinances.
We know that the ordinate of a point lying in space is it’s y-coordinate.
We know that any point lying on the two-dimensional plane will have some value of x-coordinate and some value of y coordinate.
Here, let us consider two points P and Q lying on the x-axis with its x-coordinate \[{{x}_{1}}\] and \[{{x}_{2}}\] respectively.

In the above diagram, we can observe that the points P and Q are lying on the x-axis.
Since the point P is lying next to the origin and on the x-axis, the y coordinate of origin and the point P must be equal to each other and the y coordinate of origin is equal to zero. Therefore, the y coordinate of point P is also zero.
Now, the coordinates of point P is \[\left( {{x}_{1}},0 \right)\] …………………………………………..(1)
Similarly, point Q is next to point P and on the x-axis. So, the y coordinate of point P and point Q must be equal to each other and the y coordinate of point P is equal to zero. Therefore, the y coordinate of point Q is also zero.
Now, the coordinates of point Q is \[\left( {{x}_{2}},0 \right)\] …………………………………………..(2)
From equation (1) and equation (2), we can observe that the y-coordinate of any point lying on the x-axis is equal to zero.
Therefore, the ordinate of a point lying on the x-axis is equal to zero.

Note:
In this question, one might get confused about the meaning of ordinate. So, for this type of question, we have to keep two points into consideration. That is, the ordinate of a point is its y-coordinate, and the abscissa of a point is its x-coordinate.