Question

Any point on the y-axis is of the form:
A) (x, y)
B) (0, y)
C) (y, y)
D) (x, 0)

Answer 1

Hint: We will first draw the coordinate axis with both the x-axis and y-axis. Then we will look at the y-axis and see what kind of points lie there. Thus, we will get the answer.

Complete step by step answer:
Let us first draw the axis and look at it as follows

Here, we see that x-axis and y-axis only have one common point which will be found by x = y which is only possible when x = y = 0. Hence, the origin (0, 0) lies on both the axis. Now, for the y-axis, we will either go upwards the origin in a straight line or downward in the straight line.
So, we will just have to increase or decrease the component value of y in the ordered pair (0, 0).
So, if we go upwards by a unit, we will get (0, 0 + a) that is equal to (0, a) and if we go downwards, we will get (0, 0 – a) which is equal to (0, -a). Hence, the answer would be of the form (0, y).

Hence, the correct option is (B).

Note:
The students must note that if we move over the x-axis, we will have the coordinate of the form (x, 0). Because on the x-axis, there will be no relation to y coordinate, and similarly, on the y-axis, there will be no relation to x-coordinate.
Additional Information:- The two-dimensional plane is formed by the two coordinate axes, x-axis and y-axis. Similarly, a three-dimensional plane is formed by adding one more axis that is the z-axis. The 2-dimensional plane has 4 quadrants that are the first quadrant, second quadrant, third quadrant, and fourth quadrant.