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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),(a13,b3), are

A
congruent
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B
similar
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C
equal in area
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D
none of these
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Solution

The correct option is C equal in area
If (x1,y1),(x2,y2),((x3,y3) are the vertices of triangle , then its area is
A1=12∣ ∣x1y11x2y21x3y31∣ ∣
If (a1,b1),(a2,b2),(a3,b3) are the vertices of triangle , then its area is
A2=12∣ ∣a1b11a2b21a3b31∣ ∣
A2=12∣ ∣a1a2a3b1b2b3111∣ ∣(|A|=|AT|)
A2=12∣ ∣111b1b2b3a1a2a3∣ ∣
Since, area is positive,
A2=12∣ ∣111b1b2b3a1a2a3∣ ∣
Given, ∣ ∣x1y11x2y21x3y31∣ ∣=∣ ∣111b1b2b3a1a2a3∣ ∣
A1=A2

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