Question

Abscissa of all the points on the x-axis is,
(a) 0
(b) 1
(c) 2
(d) Any number

Answer 1

Hint: We will look at the coordinate system in a cartesian plane and understand the definition of abscissa. Then we will look at points on the x-axis. We will use the definition of the coordinates of points on the x-axis to find a pattern among these points. This will allow us to eliminate some choices from the given options and obtain the correct answer.

Complete step by step answer:
The x-coordinate gives us the distance of a point from the vertical axis, which is the y-axis. The x-coordinate is also called abscissa. The y-coordinate tells us the distance of a point from the horizontal axis, which is the x-axis. The y-coordinate is also called the ordinate. The two axes, x-axis and y-axis form the xy-plane, which is also called the cartesian plane. We can see it in the figure below,

While denoting the location of a point on the xy-plane, we use the following format: $ \left( x,y \right) $ , here $ x $ is the x-coordinate and $ y $ is the y-coordinate.
We define the abscissa as the x-coordinate of a point. If we consider a point on the x-axis, then its distance from the x-axis is 0. But the distance of this point from the y-axis varies. The points on x-axis are of the type $ \left( x,0 \right) $ . The y-coordinate of the points on the x-axis is 0. So, we can see that options (a), (b), and (c) cannot be the only abscissa of all the points on the x-axis. Therefore, the correct option is (d).

Note:
We write the equation of the x-axis as $ y=0 $ and the equation for the y-axis as $ x=0 $ . In a similar way, we can write the equations of lines that are parallel to either of the axes. If a line is parallel to the x-axis, then the points on that line will have the same y-coordinate. So, we can write the equation of this line as $ y=b $ where $ b $ is the constant distance from the x-axis. Similarly, the equation of line parallel to y-axis is written as $ x=a $ where $ a $ is the constant distance from the y-axis.