Question

If $\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|=\left|\begin{array}{ccc}{a}_1& b_1& 1\\ a_2& b_2& 1\\ a_3& b_3& 1\end{array}\right|$, then the two triangles with vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ and $(a_1,b_1)$, $(a_2,b_2)$, $(a_3,b_3)$ must be congruent.

• A. True
• B. False

Answer 1

The correct option is B False

The two determinants denote twice the area of ${\Delta }^s$ whose vertices are $(x_1,y_1),(x_2,y_2)$, $(x_3,y_3)$ and $(a_1,b_1)$, $(a_2,b_2),(a_3,b_3)$. This the equality of two determinants implies that their areas are equal. But equality of the areas of two triangles does not imply that they are congruent.