Area of Triangle with Coordinates of Vertices Given
If x1 y1 ...
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.