Question

Find the distances between the following pair of points. $(b + c, c + a)$and$(c + a, a + b)$

Answer 1

Distance $d$ between two points $P(a,b)$ and $Q(c,d)$ is given by

$d=\sqrt{(a-c{)}^2+(b-d{)}^2}$

Now for the given the points $(b+c,c+a)$ & $(c+a,a+b)$

The distance between them is

$d=\sqrt{\left(\right(b+c)-(c+a){)}^2+((c+a)-(a+b){)}^2}$

$\Rightarrow d=\sqrt{(b-a{)}^2+(c-b{)}^2}$

$\Rightarrow d=\sqrt{b^2+a^2-2ab+c^2+b^2-2cb}$

$\Rightarrow d=\sqrt{a^2+2b^2+c^2-2ab-2bc}$