Question

Find the distance between the following.
(i) $(-6,7)$ and $(-1,-5)$
(ii) $(a+b,b+c)$ and $(a-b,c-b)$.

Answer 1

Distance between two points

i) $A(-6,7)$ and $B(-1-5)$

$\therefore$ Distance of AB $=\sqrt{(-1+6{)}^2+(-5-7{)}^2}=\sqrt{25+144}=13$

ii)$C(a+b,b+c)$ and $D(a-b,c-b)$

$\therefore$ Distance of CD $=\sqrt{(a-b-a-b{)}^2+(c-b-b-c{)}^2}=\sqrt{(-b{)}^2+(-b{)}^2}=\sqrt{b^2+b^2}=\sqrt{2}b$