Cartesian Plane, SMB-020 Prove the points `(1,-1), (-1,1)` and `(-sqrt3,-sqrt3)` are the vertices of a equilateral triangle. (4 marks) --- 8 WORK AREA LINES (style=lined) --- Show Answers Only `text{Proof (See worked solutions)}` Show Worked Solution `text{Let points be:}\ A(1,-1), B(-1,1) and C(-sqrt3,-sqrt3)` `text(Using the distance formula):` `d_(AB)` `=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}` `=sqrt{(1-(-1))^2+(-1-1)^2}` `=sqrt8` `d_(BC)` `=sqrt{(-1-(-sqrt3))^2+(1-(-sqrt3))^2}` `=sqrt{(-1+sqrt3)^2+(1+sqrt3)^2}` `=sqrt(1-2sqrt3+3 +1+2sqrt3+3)` `=sqrt8` `d_(AC)` `=sqrt{(1-(-sqrt3))^2+(-1-(-sqrt3))^2}` `=sqrt{(1+sqrt3)^2+(-1+sqrt3)^2}` `=sqrt(1+2sqrt3+3 +1-2sqrt3+3)` `=sqrt8` `text{Since}\ AB=BC=AC` `:. ΔABC\ text{is equilateral.}`