Naming the quadrant or axis of a point given the signs of its coordinates

In this lesson, we are given the signs of the coordinates of points. We have to find in which quadrant the given points lie or on which axis the given points lie.

We identify the quadrant from the signs of the coordinates of the points given. We also identify the axis on which the points lie if one their coordinates is a zero.

Rules to find the quadrant or axis of a point given the signs of its coordinates

• If a point has these signs of coordinates: (+, +) then the point lies in the quadrant 1.

• If a point has these signs of coordinates: (−, +) then the point lies in the quadrant 2.

• If a point has these signs of coordinates: (−, −) then the point lies in the quadrant 3.

• If a point has these signs of coordinates: (+, −) then the point lies in the quadrant 4.

• If it is like (0, +), the point lies on the positive y axis.

• If it is like (0, −), the point lies on the negative y axis.

• If it is like (+, 0), the point lies on the positive x axis.

• If it is like (−, 0), the point lies on the negative x axis.

Name the quadrant or axis of the following point whose signs are given −

(−m, n)

Solution

Step 1 − Coordinates of the given point are (−m, n).

Step 2 − Since the signs of the x and y coordinates of the point (−m, n) are (−, +) respectively.

Step 3 − Since points with the pattern (−, +) are in quadrant 2, given point lies in the quadrant 2.

Name the quadrant or axis of the following point whose signs are given.

(x, −y)

Solution

Step 1 − Coordinates of the given point are (x, −y).

Step 2 − Since the signs of the x and y coordinates of the point (x, −y) are (+, −) respectively.

Step 3 − Since points with the pattern (+, −) are in quadrant 4, given point lies in the quadrant 4.