Question

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

Answer 1

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

Let $P(b+c,c+a)$ and $Q(c+a,a+b)$

Then, distance between $P$ and $Q$ is

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