Question

The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.

• 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

$2\sqrt{2}b$

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

Let's name the points as A(a + b, b + c) and B(a - b, c - b) .

AB = $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\Rightarrow A{B}^2={(a+b-(a-b\left)\right)}^2+{(b+c-(c-b\left)\right)}^2$

$\Rightarrow A{B}^2=4b^2+4b^2=8b^2$

$\Rightarrow AB=2\sqrt{2}b$

Therefore, the distance between points (a + b, b + c) and (a – b, c – b) is $2\sqrt{2}b$ units.