The points P (2, −1), Q (−4, −1) and R (−1, 3�√3 − 1) are joined to form a triangle. Prove that triangle

Question

PQR is equilateral.

I get that you use the distance formula to find the distance between these three points, which will prove that PQR is equilateral.

I have found PQ (√36 = 6) (please correct me if i'm wrong), but i'm having trouble finding the distance between PR and QR because of '3�√3 − 1'. I'm not sure if I should add, whether to convert it to decimal beforehand, etc.
I would appreciate any help given. Thanks in advanced.

Answer 1

Plug in the formula before you get worried. The -1 goes away:

(-1-2)^2 + (3√3 − 1+1)^2
= 3^2 + (3√3)^2
= 9+27
= 36

And in any case, forget the decimal stuff -- that's just approximate. √3 is exact.