Question

The distance between the points (a + b, b + c) and (a – b, c – b) is _________ .

• A. $2\sqrt{a^2+b^2}$
• B. $2\sqrt{b^2+c^2}$
• C. $2\sqrt{2}b$
• D. $2\sqrt{a^2-c^2}$

Answer 1

The correct option is C

$2\sqrt{2}b$

Let, $A$ be $(a+b,b+c)$ and $B$ be $(a-b,c-b).$

$\because$ Distance between the points $A(x_1,y_1)\text{and}B(x_2,y_2)$ is
$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

$\therefore AB=\sqrt{(a-b-a-b{)}^2+(c-b-b-c{)}^2}=\sqrt{(-2b{)}^2+(-2b{)}^2}=\sqrt{8b^2}AB=2\sqrt{2}b$

$\therefore$ Distance between the points = $2\sqrt{2}b$.