Question

Find the distance between the following pair of points:

 (a + b, b + c) and (a – b, c – b)

Answer 1

The distance d between two points (x₁, y₁) and (x₂, y₂) is given by the formula.

`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`

 The two given points are (a + b, b + c) and (a - b, c - b)

`d = sqrt((a + b - a + b)^2 + (b + c - c + b)^2)`

`= sqrt((2b)^2 + (2b)^2)`

`= sqrt(4b^2 + 4b^2)`

`= sqrt(8b^2)`

`d = 2bsqrt2`

Hence the distance is `2bsqrt(2)` units.