Question

Which point lies on the X-axis?
A. \[(0,3)\]
B. \[( - 3,0)\]
C. \[( - 5, - 1)\]
D. \[(4, - 3)\]

Answer 1

Hint: We use the concept of two dimensional plane and use the definition of a point lying on the axes of the plane to check which of the given points lie on the X-axis.
* A two-dimensional plane has two axes i.e. X-axis and Y-axis which are perpendicular to each other at the point of origin. Any point in a two-dimensional space can be written as \[(x,y)\] where ‘x’ is the abscissa and ‘y’ is the ordinate. The value of ‘x’ is the intercept or the distance on x-axis and the value of ‘y’ is the intercept or the distance on y-axis.
* If any point in the plane has coordinates \[(x,y)\], then the general form of point lying on the x-axis is \[(x,0)\] where ‘x’ can be any integer and general form of point lying on the y-axis is \[(0,y)\] where ‘y’ can be any integer.

Complete step-by-step solution:
We have to check from four given points which lie on the x-axis.
Since we know any pointy lying on the x-axis is of the form \[(x,0)\] where ‘x’ can be any integer, we choose the option which has its ordinate value as zero i.e. 0.
We are given the points \[(0,3),( - 3,0),( - 5, - 1),(4, - 3)\]
Since the only point that has value of ordinate as 0 is \[( - 3,0)\]
The other options \[(-5, -1), (4,-3)\] does not lie on both the x or y axis because none of the coordinates is 0.
\[\therefore \]The point \[( - 3,0)\] lies on the X-axis

\[\therefore \]Option B is correct.

Note: Many students make the mistake of choosing option A i.e.\[(0,3)\] as they get confused with the fact that the point lying on the X-axis will have x-coordinate as zero. Keep in mind the coordinates give us the distance of the point from respective axes and here we look for distance on y-axis equal to zero as we want the point on X-axis.