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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∣ ∣
∣ ∣ ∣∣ ∣ ∣x1y11x2y21x3y31∣ ∣ ∣∣ ∣ ∣=∣ ∣∣ ∣111b1b2b3a1a2a3∣ ∣∣ ∣
∣ ∣ ∣∣ ∣ ∣x1y11x2y21x3y31∣ ∣ ∣∣ ∣ ∣=∣ ∣∣ ∣a1b11a2b21a3b31∣ ∣∣ ∣
both triangle have equal area


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