Question

一个等边三角形ABC的两个顶点B(0,0),C(1,3),顶点A的坐标是

Answer 1

设A(m,n)

∵等边

∴AB=BC=AC

AB^2=BC^2=AC^2

∴m^2+n^2 =10=(m-1)^2+(n-3)^2

解得m= - (3√201 +15)/4 n=(15+√201)/4

或m=(3√201 -15)/4 n=(15-√201)/4