If the value of is zero for three points

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

If the value of ∣x1y11x2y21x3y31∣\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix} is zero for three points (x1,y1), (x2,y2), (x3,y3)(x_1,y_1),\,(x_2,y_2),\,(x_3,y_3), what can be concluded about these points? (a) They form an equilateral triangle (b) They are collinear (c) They form a right-angled triangle (d) The centroid of the triangle formed by them is at the origin

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