Question

In which quadrant does the point lie if the x-coordinate is negative and y-coordinate is positive?

Answer 1

Hint: Assume a point whose x-coordinate is negative and y-coordinate is positive. Take the x-axis and y-axis separately. On the x-axis, for negative x coordinates, we have to go beyond origin towards the negative x coordinates. On the y-axis, for positive y coordinates, we have to go above the origin towards the positive y coordinates. Now, observe the parts where the negative x coordinate and positive y coordinate falls and then predict the quadrant where the point having negative x-coordinate and positive y-coordinate falls.

Complete step-by-step solution:
According to the question, it is given that a point is having a negative x coordinate and positive y coordinate.
Let us assume a point A whose x coordinate be -p and y coordinate be q. The coordinate of the point is,
A= (-p, q) ……………………(1)
We know that the points in \[{{1}^{st}}\] quadrant have positive x coordinates and also positive y coordinates.
Here, we have the point A which negative x coordinate and positive y coordinate.
For negative x coordinates, we have to go beyond origin towards the negative x coordinates.
Let us visualize using a diagram.

We also have to think about the y- coordinates which are positive here. For positive y coordinates, we have to go above the origin towards the positive y coordinates.
Let us visualize using a diagram.

Now, we have to visualize both the negative x coordinate and positive y coordinate at a time.
Let us visualize using a diagram.

From the figure, we can see that only quadrant II will have the points having negative x coordinates and positive y coordinates.
Therefore, the points having negative x-coordinates and positive y-coordinates must lie in quadrant II.

Note: For this type of question, where we are given the sign of the x-coordinate and y coordinate of a point and we have to find the corresponding quadrant of the point, we must remember the facts that both of the x-coordinate and y-coordinate of a point are positive if the point is lying the first quadrant. For a point lying in the second quadrant, the x-coordinate is negative while the y-coordinate is positive. Similarly, for a point lying in the third quadrant, both of the x-coordinate and y-coordinate are negative. At last, for a point lying in the fourth quadrant, the x-coordinate is positive while the y-coordinate is negative.