Practice question
Question
An equilateral triangle has each side equal to a. If the co-ordinates of its vertices are (x₁, y₁); (x₂, y₂): (x₃, y₃) then the square of the determinant vmatrix x_1 & y_1 & 1 x_2 & y_2& 1 x_3 & y_3 & 1 vmatrix equals:
Explanation
We know that area =½|det| where det=|x₁ y₁ 1;x₂ y₂ 1;x₃ y₃ 1|. Equilateral area=√3/4 a². So ½|det|=√3/4 a², det²=3a⁴/4.
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