On which axis do the following points lie?

Solution:

According to the Rectangular Cartesian Co-ordinate system of representing a point (x, y),

If $x>0, y>0$ then the point lies in the $1^{\text {st }}$ quadrant

If $x<0, y>0$ then the point lies in the $2^{\text {nd }}$ quadrant

If $x<0, y<0$ then the point lies in the $3^{\text {rd }}$ quadrant

If $x>0, y<0$ then the point lies in the $4^{\text {th }}$ quadrant

But in case

If $x=0, y \neq 0$ then the point lies on the $y$-axis

If $y=0, x \neq 0$ then the point lies on the $x$-axis

(i) Here the point is given to be $P(5,0)$. Comparing this with the standard form of

 

$(x, y)$ we have

$x=5$

$y=0$

Here we see that $y=0, x \neq 0$

Hence the given point lies on the $x$-axis

(ii) Here the point is given to be $Q(0,--2)$. Comparing this with the standard form of $(x, y)$ we have

$x=0$

$y=-2$

Here we see that $x=0, y \neq 0$

Hence the given point lies on the $y$-axis

(iii) Here the point is given to be $R(-4,0)$. Comparing this with the standard form of $(x, y)$ we have

$x=-4$

$y=0$

Here we see that $y=0, x \neq 0$

Hence the given point lies on the $x$-axis

(iv) Here the point is given to be $S(0,5)$. Comparing this with the standard form of $(x, y)$ we have

$x=0$

$y=5$

Here we see that $x=0, y \neq 0$

Hence the given point lies on the $y$-axis