Chapter 1.8, Problem 26E

To determine

To tell : by looking at the coordinate of a point whether the point in on the $x$ -axis or on the $y$ -axis.

Answer to Problem 26E

If the point is of the form $\left(x,\text{ 0}\right)$ then it is on the $x$ -axis and if it is of the form $\left(0,y\right)$ then the point is on the $y$ -axis.

Explanation of Solution

Solution :

If the $y$ -coordinate of the point is 0 and the point is of the form $\left(x,\text{ 0}\right)$ then the point is on the $x$ -axis. And,

If $x$ -coordinate of the point is 0 and the point is of the form $\left(0,y\right)$ then the point is on the $y$ -axis.

Hence,

If the point is of the form $\left(x,\text{ 0}\right)$ then it is on the $x$ -axis and if it is of the form $\left(0,y\right)$ then the point is on the $y$ -axis.