Question

The distance between the points A(0,$\sqrt{3}$ and B $(\sqrt{3}+1,1)$ is ________ units.

• A. 2
• B. $2\sqrt{2}$
• C. 3
• D. $\sqrt{2}$

Answer 1

The correct option is B

$2\sqrt{2}$

Using Distance Formula we have,

$AB=\sqrt{(\sqrt{3}+1-0{)}^2+(1-\sqrt{3}{)}^2}$

=$\sqrt{(1+\sqrt{3}{)}^2+(1-\sqrt{3}{)}^2}$

$=2(1+3)(\because (a+b{)}^2+(a-b{)}^2=2(a^2+b^2\left)\right)$

=$\sqrt{2\left(2^2\right)}$

=$2\sqrt{2}$units.