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Question
The area of a triangle whose vertices are (1, 2), (-3, 4) and (-5, 6) is
The area of a triangle whose vertices are (1, 2), (-3, 4) and (-5, 6) is
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Solution
The correct option is B 2 sq. units
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 =∣∣∣(1)(4−6)+(−3)(6−2)+(−5)(2−4)2∣∣∣=∣∣∣−2−12+102∣∣∣=42=2 sq units
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 =∣∣∣(1)(4−6)+(−3)(6−2)+(−5)(2−4)2∣∣∣=∣∣∣−2−12+102∣∣∣=42=2 sq units
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