3
Question
The area of a triangle with the vertices (1,2),(3,4) and (5,6) is _________
The area of a triangle with the vertices (1,2),(3,4) and (5,6) is _________
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Solution
The correct option is A 0
Area of a triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is ∣∣∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)2∣∣∣
Hence, substituting the points (x1,y1)=(1,2) ; (x2,y2)=(3,4) and (x3,y3)=(5,6) in the area formula, we get
Area of triangle ABC =∣∣∣(1)(4−6)+(3)(6−2)+5(2−4)2∣∣∣=∣∣∣−2+12−102∣∣∣=0
Area of a triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is ∣∣∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)2∣∣∣
Hence, substituting the points (x1,y1)=(1,2) ; (x2,y2)=(3,4) and (x3,y3)=(5,6) in the area formula, we get
Area of triangle ABC =∣∣∣(1)(4−6)+(3)(6−2)+5(2−4)2∣∣∣=∣∣∣−2+12−102∣∣∣=0
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