find the distance between the points (1,Square root of 3), (-1,1)

Question

The answer to this question was d=square root (8-2square root of 3). But I keep getting  a different answer.

Answer 1

The equation to find the distance ( d ) between two points (x₁, y₁) and (x₂, y₂) is:

 

 d²  = (x₂ - x₁)² + (y₂ - y₁)² 

 

 The points that we want to find the distance between them are : ( 1, sqrt(3) ) and ( -1, 1)

 

so d² = ( -1 -1)² + (1- sqrt(3) )²  = ( - 2 )² + (1- sqrt(3) )² = 4 +  (1- sqrt(3) )² 

 

 now let's simplify the term  (1- sqrt(3) )² in our equation, 

(1- sqrt(3) )² =  (1- sqrt(3) )* (1- sqrt(3) ) = 1 - 2*sqrt(3) +3, put that back in the equation of d²

 

d² = 4 + 1 - 2*sqrt(3) +3 = 8 - 2*sqrt(3)

 

taking the square root of both sides of the equation to find our distance d we get

d = sqrt ( 8 - 2*sqrt(3)) 

Answer 2

d = √(8 - 2√3) is the correct distance using the distance formula d = √[(y₂-y₁)² + (x₂-x₁)²]

 

What distance formula were you using, and what answer were you getting?