Question

Which point lies on Y-axis?
(a). \[\left( 4,0 \right)\]
(b). \[\left( 0,4 \right)\]
(c). \[\left( -8,0 \right)\]
(d). \[\left( 0,-8 \right)\]

Answer 1

Hint: First, one should know the form of the coordinate system which is given by \[\left( x,y \right)\] . So, while seeing the option compare with this given form and accordingly, plot the point on the graph to know which point lies on which axis.

Complete step-by-step answer:

A coordinate system is a two-dimensional system consisting of vertical and horizontal lines known as axes. The figure is as shown below:

Now, here vertical line is indicated as Y-axis and horizontal line is indicated as X-axis. Here, the centre is called Origin where x-axis and y-axis intersect.
An ordered pair contains the coordinates of one point in the coordinate system. It is named by its ordered pair of the form of \[\left( x,y \right)\] . The first number will always correspond to the X-axis and the second number will always correspond to the Y-axis. The origin is denoted by \[\left( 0,0 \right)\] .
Now, we are asked to find out of the given option which option lies on Y-axis. So, Y-axis means above the origin which is called the positive Y-axis and below the origin part which is known as the negative Y-axis.
So, here taking the first option (a): \[\left( 4,0 \right)\] Here, x-coordinate is 4 and y-coordinate is 0. So, by plotting this point in graph, we get as

So, this point lies on horizontal line ie. X-axis. So, this option is not correct.
Taking option (b): \[\left( 0,4 \right)\] Here, 0 is on x-coordinate and 4 is y-coordinate. So, we get in graph as

As y-coordinate is number and x-coordinate is 0 it refers to the y-axis point. So, this option is correct.
Taking option (c): \[\left( -8,0 \right)\] Here again it is similar to that of option (a) i.e. y-coordinate is 0 and x-coordinate is a number. So, this point will be represented on X-axis.

 So, this option is not correct.
Now, option (d): \[\left( 0,-8 \right)\] So, by plotting this point on a graph we can identify that this point lies on the y-axis.

So, this option is correct.
Thus, we get two points which lie on the Y-axis are \[\left( 0,4 \right)\] , \[\left( 0,-8 \right)\] .
Hence, option (b) and (d) are correct.

Note: Sometimes mistakes are made while either of coordinate i.e. x-coordinate or y-coordinate is zero. So, remember the form of this coordinate system which is given by \[\left( x,y \right)\] . Also, another method is that if either of x or y coordinates is zero then the remaining coordinate is the answer. For example: If we have a point \[\left( 0,1 \right)\] then x-coordinate is 0 so this point lies on the Y-axis. Similarly, we can easily find which point lies on which axis.