Question

Find the distance between the points $(a,b)$ and $(-a,-b)$

Answer 1

Let point is $A(a,b)$ and $B(-a,-b)$ then distance between them
$\begin{array}{cc}AB& =\sqrt{(-a-a{)}^2+(-b-b{)}^2}\\ & =\sqrt{(-2a{)}^2+(-2b{)}^2}\\ & =\sqrt{4a^2+4b^2}\\ & =\sqrt{4(a^2+b^2)}\end{array}$
$=2\sqrt{a^2+b^2}$