Area of Triangle with Coordinates of Vertices Given
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Question
If ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣
then two triangles with vertices (x1,y1),(x2,y2),(x3,y3) and (a1,b1),(a2,b2),(a3,b3) are
A
equal in area
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B
similar
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C
congurent
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D
with different areas
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Solution
The correct option is A equal in area ∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣⇒12∣∣
∣∣x1y11x2y21x3y31∣∣
∣∣=12∣∣
∣∣a1b11a2b21a3b31∣∣
∣∣TrianglesareequalinareaHence,theoptionAiscorrectanswer.