Question

Find the distance between the following pair of points:

`(sqrt(3)+1,1)` and `(0, sqrt(3))`

Answer 1

Step 1: Formula

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

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

Step 2: Substitute values

`x_1 = sqrt3 + 1, y_1 = 1, x_2 = 0, y_2 = sqrt3`

`d = sqrt((0 - (sqrt3 + 1))^2 + (sqrt3 - 1)^2)`

Step 3: Simplify

`d = sqrt((sqrt3 + 1)^2 + (sqrt3 - 1)^2)`

`= sqrt((3 + 2sqrt3 + 1) + (3 - 2sqrt3 + 1))`

`= sqrt((4 + 2sqrt3) + (4 - 2sqrt3))`

`= sqrt8`

Step 4: Simplify further

`d = 2sqrt2`