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)

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`text{Proof (See worked solutions)}`

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`ΔOAB\ text{is equilateral}\ \ =>\ \ OA=AB=OB=8`

`text{Let}\ C=(0,4)`

`text{Consider}\ ΔOCB:`

`B=(4,4sqrt(2))`

`:.k=4sqrt(2)`