Question

A triangle has vertices A_i (x_i, y_i) for i = 1, 2, 3. Then the determinant 

\(\triangle = \begin{vmatrix}x_2-x_3&y_2-y_3&y_1(y_2 - y_3) + x_1(x_2 - x_3)\\x_3-x_1&y_3 - y_1 &y_2(y_3 - y_1) + x_2(x_3 - x_1)\\x_1-x_2&y_2-y_2&y_3(y_1-y_2) + x_3(x_1 -x_2)\end{vmatrix} = 0\) means

(a) the medians for triangle A₁A₂A₃ are concurrent

(b) the triangle A₁A₂A₃ is right angled at A₃

(c) the triangle A₁A₂A₃ equilateral triangle

(d) altitudes of the triangle A₁A₂A₃ are concurrent

Answer 1

(d) altitudes of the triangle A₁A₂A₃ are concurrent