Use the distance formula to find the distance between the two points
(a, b) (b, a).
$\displaystyle A(a,b)$ and $\displaystyle B(b,a)$
The distance between the two points A and B:
$\displaystyle |\vec{AB}|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}=\sqrt{(b-a)^2+(a-b)^2}=\sqrt{2}.|a-b| $
I don't know is it true or false ? So if it's false, please tell me !
Username lovemath got the right answer. I tried getting the right answer over and over again but ended up with something totally different. How does the answer become sqrt{2}*|a - b|? In the radicand we have (a - b)^2 + (b - a)^2, which equals 2a^2 - 4ab +2b^2
$\displaystyle \sqrt{2^2}= \sqrt{4}= 2$ $\displaystyle \sqrt{(-2)^2}= \sqrt{4}= 2$. Since $\displaystyle \sqrt{x}$ is defined as "the non-negative number a such that $\displaystyle a^2= x$, if x is itself non-negative, then $\displaystyle \sqrt{x^2}= x$ but if x is negative, $\displaystyle \sqrt{x^2}= -x$. In either case $\displaystyle \sqrt{x^2}= |x|$.