Question

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of the point C are (0, -3). If origin is the mid-point of the base BC, find the coordinates of the points A and B.
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Answer 1

$Coordinate = (0,3) (x,0)$

$AB = \sqrt{(0 - x}) ^{2} + \sqrt{(3 - 0) ^{2} }$

$AB = \sqrt{ {x }^{2} + 9 }$

$BC = \sqrt{(0 - 0) ^{2} + ( - 3 - 3) ^{2} }$

$BC = \sqrt{36}$

$AB = BC$

$\sqrt{ {x}^{2} + 9} = \sqrt{36}$

${x}^{2} + 9 = 36$

${x}^{2} = 27$

$x = ±3 \sqrt{3}$

$Coordinate \: A =(3 \sqrt{3} ,0)$