Area of Triangle with Coordinates of Vertices Given
If x1 y1 ...
Question
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣ = ∣∣
∣∣111b1b2b3a1a2a3∣∣
∣∣ then the two triangles whose vertices are (x1,y1),(x2,y2),(x3,y3) and (a1,b1),(a2,b2),(a3,b3) are
A
congruent
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B
similar
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C
equal in areas
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D
right angled triangles
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Solution
The correct option is C equal in areas Area of triangle whose vertices are (x1,y1),(x2,y2),(x3,y3) is
=∣∣
∣
∣∣12∣∣
∣
∣∣x1y11x2y21x3y31∣∣
∣
∣∣∣∣
∣
∣∣
And are of triangle whose vertices are (a1,b1),(a2,b2),(a3,b3) is
=12∣∣
∣∣∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣∣∣
∣∣
As ∣∣
∣
∣∣x1y11x2y21x3y31∣∣
∣
∣∣=∣∣
∣∣111b1b2b3a1a2a3∣∣
∣∣