Question

On a cartesian plane, $(p,q)$ and $(q,p)$ represent two different points.

• A. For all values of $p$ and $q$
• B. Only when $p\ne q$

Answer 1

The correct option is B Only when $p\ne q$

First we represent $(p,q)$ and $(q,p)$ on a cartesian plane for two cases:

$\underset{–}{\text{Case1:}p=q}$
Suppose $p=q=3$, then
$(p,q)=(q,p)=(3,3)$

In this case $(p,q)$ and $(q,p)$ represent the $\underset{–}{\text{same point}}$.

$\underset{–}{\text{Case2:}p\ne q}$
Suppose $p=3$ and $q=5$, then

In this case $(p,q)$ and $(q,p)$ represent the $\underset{–}{\text{different points}}$.

$\therefore$ $(p,q)$ and $(q,p)$ represent different points only when $p\ne q$.