The base BC of an equilateral triangle ABC lies on y-axis. I the coordinates of the point C ate(0,-3). The origin is the midpoint of the base BC, find the coordinates of the points A and B?

1 Answer
CW
Mar 20, 2018

see explanation.

Explanation:

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Given base #BC# lies on y-axis, #C=(0,-3)#, and origin #O(0,0)# is the midpoint,
#=> OC=3# units,
#=> OB=OC=3# units,
#=># coordinates of #B=(0,3)#
#=> BC=OB+OC=3+3=6# units
given #DeltaABC# is equilateral,
#=> AO# is perpendicular to #BC and AB=BC=6# units,
#=> DeltaAOB# is a right triangle,
By Pythagorean theorem, we know,
#=> AO^2=AB^2-OB^2#,
#=> AO^2=6^2-3^2=36-9=27#,
#=> AO=sqrt27=sqrt(9xx3)=3sqrt3# units
#=># coordinates of #A(x,y)=(-3sqrt3,0)#
Similarly, coordinates of #A'(x',y')=(3sqrt3,0)#

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