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Question

Prove that area if triangle ABC with vertices A(3,2),B(11,8),C(8,12) is 25 square units.

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Solution

Given that,
A=(3,2)
B=(11,8)
C=(8,12)

Area(ABC)=12|x1(y2y3)+x2(y3y1)+x3(y1y2)|

=12|3(812)+11(122)+8(28)|

=12|3(4)+11(10)+8(6)|

=12|12+11048|

=12(50)

=25 Sq.units

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