State whether the following statements are true or false . Justify your answer. Points A(3,1),B(12,−2) and C(0,2) cannot be the vertices of a triangle .
A
True
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B
False
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Solution
The correct option is A True Points A,B,C can form a triangle if the sum of any two sides is greater than the third side. AB2=(x2−x1)2+(y2−y1)2 ⇒AB2=(12−3)2+(2−1)=81+9=90 ⇒AB=3√10 units BC2=(0−12)2+[2−(−2)]2=144+16=160 ⇒BC=4√10 units AC2=(0−3)2+(2−1)29+1=10 ⇒AC=√10 units ∴AC=√10 units , AB=3√10 units Now , AB+AC=√10+3√10=4√10 units =BC So , A,B,C points cannot form a Δ.