Question

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

Answer 1

Hint: In this question, we have to mainly focus on finding the equation of the x-axis. Once you get the equation of x-axis, figure out the constraint on x and find the number which satisfies the constraint.

Complete step-by-step answer:

Before moving to the solution let us discuss the meaning of abscissa. Abscissa of a point refers to the x-coordinate of the point. For example the abscissa of the point (a,b) is a.

Now moving on to the solution, let us first try to get the equation of the x-axis.

We know that the slope is defined as $\text{ }m=\tan \theta $, where $\theta$ is the angle made by the line with positive x-axis in an anti-clockwise direction.

So, for x-axis $\theta ={{0}^{c}}$ hence, making the slope of x-axis:

$m=\tan \theta =\tan {{0}^{c}}=0$

We know, the general equation of the line can be written as:

$y=mx+c$

So, the equation of x-axis becomes:

$y=0.x+c$

$\Rightarrow y=0+c$

$\Rightarrow y=c...........(i)$

Here, c is a constant and to eliminate this, we need a point lying on the x-axis and we know the x-axis passes through the origin so the point on the line is O (0, 0).

Putting in the equation $\text{ }(i)$ , we get

$y=c$

$\Rightarrow 0=c$

$\therefore c=0$

Therefore, the equation of the x-axis comes out to be $y=0$ .

Now it is clear from the equation that there is no constraint on x, i.e., the abscissa of the points lying on the x-axis can be any number. Hence the answer to the above question is option (d).

Note: Alternately, you can assume any three random points lying on the x-axis and reach an answer. Also avoid using intercept form of line for the lines parallel to x-axis and y-axis as you may get one of the intercepts to be infinity.