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Question

If ∣ ∣x1y11x2y21x3y31∣ ∣=∣ ∣a1b11a2b21a3b31∣ ∣, then the two triangles with vertices (x1,y1),(x2,y2),(x3,y3) and (a1,b1), (a2,b2), (a3,b3) must be congruent.

A
True
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B
False
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Solution

The correct option is B False
The two determinants denote twice the area of Δs whose vertices are (x1,y1),(x2,y2), (x3,y3) and (a1,b1), (a2,b2),(a3,b3). 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.

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