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. |
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