Question

Find the distance between P and Q. If $\frac{a-b}{2}=9$, $P(a,b),Q(b,a)$.

• A. $18$ units
• B. $18\sqrt{2}$ units
• C. $\sqrt{18}$ units
• D. None of the above

Answer 1

Answer: (B)

$18\sqrt{2}$ units

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

The given co-ordinates are $P(a,b)$ and $Q(b,a)$

$\therefore$ by distance formula, $PQ=\sqrt{(a-b{)}^2+(b-a{)}^2}$

$\frac{a-b}{2}=9$ ...........(given) $⟹a-b=18$, $PQ=\sqrt{{18}^2+(-18{)}^2}=\sqrt{{18}^2(1+1)}=18\sqrt{2}$

So, option B is correct.