Question

Let $p,q,r,s$ be the distances from origin of the points $A(2,6),B(3,4),C(4,5)$ and $D(-2,5)$ respectively. Which one of the following is a whole number?

• A. $p$
• B. $q$
• C. $r$
• D. $s$

Answer 1

The correct option is B $q$

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

Now, calculating the distance of each point from origin

$p=AO=\sqrt{(2-0{)}^2+(6-0{)}^2}=\sqrt{40}q=BO=\sqrt{(3-0{)}^2+(4-0{)}^2}=5r=CO=\sqrt{(4-0{)}^2+(5-0{)}^2}=\sqrt{41}s=DO=\sqrt{(-2-0{)}^2+(5-0{)}^2}=\sqrt{29}$

$\therefore$ BO is a whole number i.e,q.