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Question

The area of ∆ABC with vertices A(1, −1), B(−4, 6) and C(−3, −5) is

(a) 52 sq units
(b) 27 sq units
(c) 48 sq units
(d) 24 sq units

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Solution

(d) 24 sq units
The given points are A1, -1, B-4, 6 and C-3, -5.
Here, x1=1, y1=-1, x2=-4, y2=6 and x3=-3, y3=-5
Therefore,
Area of ABC=12x1y2-y3+x2y3-y1+x3y1-y2
=1216+5+-4-5+1+-3-1-6=1211+16+21=12×48=24 sq units

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