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Question

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=(x2x1)2+(y2y1)2
AB2=(123)2+(21)=81+9=90
AB=310 units
BC2=(012)2+[2(2)]2=144+16=160
BC=410 units
AC2=(03)2+(21)29+1=10
AC=10 units
AC=10 units , AB=310 units
Now , AB+AC=10+310=410 units =BC
So , A,B,C points cannot form a Δ.

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