Find the distance between these three points to prove that it is an equilateral triangle (0,1) (4,1) (2,1-2(3^(1/2)))a

Question

I can not figure out how to solve this please help

Answer 1

Call the three points A, B and C. To work out the distances between them (AB, AC and BC), we need to use Pythagoras' theorem on the xy coords. Take the difference between the y coords and square it, then the difference between the x coords and square that. Add them together and take the square root to get the distance between them. AB=sqrt(0+16)=4; AC=sqrt((-2(3^1/2))^2+4)=sqrt(12+4)=sqrt(16)=4; BC=sqrt(12+4)=4. So all three sides have a length of 4, making it an equilateral triangle.