Coordinate Geometry
Geometry
Level
pending
Can an equilateral triangle be drawn on a Cartesian plane such that all its vertices have rational coordinates?
no
yes
cannot be determined
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1 solution
we know that area of equilateral triangle is 4 3 × a 2 , where a is the side length of the triangle. so if all the coordinates are rational then area of that triangle is also rational using determinant we can prove that, also side length is also rational by using Distance Formula. so if triangle is equilateral, area must be irrational as multiplied by 3 ,so triangle can't be equilateral.