Cartesian Plane, SMB-021 An equilateral triangle has vertices `O(0,0)` and `A(8,0)` as shown in the diagram below. Find `k` if the coordinates of the third vertex are `B(4,k)`. (4 marks) --- 8 WORK AREA LINES (style=lined) --- Show Answers Only `text{Proof (See worked solutions)}` Show Worked Solution `ΔOAB\ text{is equilateral}\ \ =>\ \ OA=AB=OB=8` `text{Let}\ C=(0,4)` `text{Consider}\ ΔOCB:` `OB^2` `=OC^2+CB^2` `64` `=16+CB^2` `CB^2` `=48` `CB` `=sqrt(48)` `=4sqrt(2)` `B=(4,4sqrt(2))` `:.k=4sqrt(2)`