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

Given:

The given pair of points is $(a + b, b + c)$ and $(a – b, c – b)$.

To do:

We have to find the distance between the given pair of points.

Solution:

We know that,

The distance between two points \( \mathrm{A}\left(x_{1}, y_{1}\right) \) and \( \mathrm{B}\left(x_{2}, y_{2}\right) \) is \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \).

Therefore,

 The distance between \( (a+b, b+c) \) and \( (a-b, \) \( c-b) \) \( =\sqrt{(a-b-a-b)^{2}+(c-b-b-c)^{2}} \)

\( =\sqrt{(-2 b)^{2}+(-2 b)^{2}} \)

\( =\sqrt{4 b^{2}+4 b^{2}} \)

\( =\sqrt{8 b^{2}} \)

\( =2 \sqrt{2} b \)

The distance between the given points is $2\sqrt{2}b$.