question_answer

The points (2, 2), (6, 3) and (4, 11) are the vertices of

A) an equilateral    

B) a right angled triangle

C) an isosceles triangle

D) a scalene triangle

Correct Answer: D

Solution :

\[AC=\sqrt{{{(11-2)}^{2}}+{{(4-2)}^{2}}}\]

\[=\sqrt{81+4}=\sqrt{85}\]

\[BC=\sqrt{{{(11-3)}^{2}}+{{(4-6)}^{2}}}\]

\[=\sqrt{{{8}^{2}}+{{2}^{2}}}=\sqrt{64+4}=\sqrt{68}\]

\[AB=\sqrt{{{(3-2)}^{2}}+{{(6-2)}^{2}}}\]

\[=\sqrt{1+16}=\sqrt{17}\]

\[\therefore \]      \[AC\ne BC\ne AB\]

Hence, the points are the vertices of a scalene triangle.