A) equilateral triangle
B) right-angled triangle
C) isosceles right-angled triangle
D) None of the above
Correct Answer: C
Solution :
| [c] Let \[A(4,0),\,\,B(-1,-1),\,\,C(3,5)\] |
| \[AB=\sqrt{{{(-1-4)}^{2}}+{{(-1-0)}^{2}}}=\sqrt{26}\] |
| \[BC=\sqrt{{{(3+1)}^{2}}+{{(5+1)}^{2}}}=\sqrt{52}\] |
| \[AC=\sqrt{{{(3-4)}^{2}}+{{(5-0)}^{2}}}=\sqrt{26}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,A{{B}^{2}}+A{{C}^{2}}=B{{C}^{2}}\] and \[AB=AC\] |
| Hence, triangle is an isosceles right angled triangle. |
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