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Question
The area of a triangle whose vertices are (-5, -1), (3, -5), (5, 2) is :
The area of a triangle whose vertices are (-5, -1), (3, -5), (5, 2) is :
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Solution
The correct option is B 32 square 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)=(−5,−1) ; (x2,y2)=(3,−5) and (x3,y3)=(5,2) in the area formula, we get
Area of triangle ABC =∣∣∣(−5)(−5−2)+(3)(2+1)+5(−1+5)2∣∣∣=∣∣∣35+9+202∣∣∣=642=32squnits
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)=(−5,−1) ; (x2,y2)=(3,−5) and (x3,y3)=(5,2) in the area formula, we get
Area of triangle ABC =∣∣∣(−5)(−5−2)+(3)(2+1)+5(−1+5)2∣∣∣=∣∣∣35+9+202∣∣∣=642=32squnits
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