A(−2,0),B(2,3),C(5,−1)
BA=⟨−2−2,0−3⟩=⟨−4,−3⟩
BC=⟨5−2,−1−3⟩=⟨3,−4⟩
BA⋅BC=−4(3)+(−3)(−4)=0 Then BA⊥BC, and we see that the triangle ABC with vertices A(−2,0),B(2,3),C(5,−1) is a right triangle.
∣BA∣=(−4)2+(−3)2=5
∣BC∣=(3)2+(−4)2=5
AreaABC=21∣BA∣∣BA∣
=21(5)(5)=12.5(units2)
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