Question

The coordinate axes divide the plane into ____.
(a) One part
(b) Two parts
(c) Three parts
(d) Four parts

Answer 1

Hint: We will consider a 2 dimensional space and we will draw two axes on it. As a result we will get the required division of the plane and after that we will record that number as the right answer.

Complete step-by-step solution -
In Mathematics we come across the two dimensional space. This is a kind of a space which consists of two axes. These two coordinates are called x axis and y axis. Now, we consider a plane in the form of a graph and we will draw these coordinates one by one. First we will draw the x axis. For this we will draw a horizontal line as shown below.

As we can clearly see that this axis has divided the plane into two parts. Now, we will draw the y axis means a line which is perpendicular to the x axis. Thus, we get

Now, we can clearly notice that the two axes together are dividing the plane into four equal parts. The division of this plane gives rise to the four quadrants namely, first, second, third and fourth quadrant. In the first quadrant we will have positive values of x and y both. In the second quadrant we will have the values of x as negative but the values of y as positive. In the third quadrant we will still have negative values of x but this time the values of y will also be negative while in the fourth quadrant we have both x and y values as negative. The required diagram with points on it is shown below.

Therefore, the coordinate axes divide the plane into four parts. Hence the correct option is (d).

Note: If we need to show the two axes then for that it is compulsory to consider the two dimensional space. Otherwise, the answer will be considered as a wrong answer. We can make a mistake here by considering only one axis and then marking option (b) as the correct answer. We have been asked ‘axes’ and not ‘axis’ in the question, so we must be careful. We can see that the division of the points has a space of 1 unit between them. Whenever we plot the points on the graph line we will take care of the fact that all the lines will be divided into equal units whether we are taking the division as 1 unit or 10 units.