Question

Abscissa of a point is positive in …………………… quadrant.
(A) I and II
(B) II and III
(C) III and IV
(D) IV and I

Answer 1

Hint: We can observe that on moving rightward from the origin we will get the positive x-coordinate that is any point lying on the line OX will have a positive coordinate where O is the origin. Now, check the quadrants that have the line OX as common.

Complete step by step answer:
According to the question, we are asked to get the quadrants where the abscissa of a point can be positive.
First of all, we need the meaning of abscissa.
We know the abscissa of a point is its x-coordinate …………………………………….(1)
Let us observe the coordinate axes.

In the above diagram, we can observe that the line OX is the line that has points with positive x-coordinates.
We have to pick the quadrants in which a point has a positive x-coordinate and we don’t have any restriction on the y-axis. So, we have to pick up the quadrants having positive x-coordinate and it may or may not have positive y-coordinate.
In the diagram, we can observe that the line OX is common to both the first quadrant and fourth quadrant, and each point that is lying on the line is having positive x-coordinates.
Therefore, quadrant first and quadrant fourth have positive abscissa.
Hence, the correct option is (D).
Note:
In this question, one might make a silly mistake and pick up those quadrants where the y-coordinate of a point is positive. This is wrong because we are asked to find the quadrants where the abscissa of a point is positive and the abscissa of a point is its x-coordinate.