A) a right angled triangle
B) an acute angled triangle
C) an obtuse angled triangle
D) None of the above
Correct Answer: A
Solution :
Let the vertices of triangle be \[A(4,0),\] \[B(-1,-1)\] and \[C(3,5)\] Now, \[AB=\sqrt{{{(-1-4)}^{2}}+{{(-1-0)}^{2}}}\] \[=\sqrt{25+1}=\sqrt{26}\] \[AC=\sqrt{{{(3-4)}^{2}}+{{(5-0)}^{2}}}\] \[=\sqrt{1+25}=\sqrt{26}\] and \[BC=\sqrt{{{(3+1)}^{2}}+{{(5+1)}^{2}}}\] \[=\sqrt{16+36}=\sqrt{52}\] \[\Rightarrow \] \[AB=AC\] Also, \[{{(BC)}^{2}}={{(AB)}^{2}}+{{(AC)}^{2}}\] Hence, its right angled triangle.
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