A) right angled
B) isosceles
C) equilateral
D) None of the above
Correct Answer: C
Solution :
[c] Let \[P\,(1,\,1),Q\,(-1,\,-1)\]and \[R\,(-\,\sqrt{3},\,\sqrt{3})\]are vertices of \[\Delta PQR.\] \[\therefore \] \[PQ=\sqrt{{{(1+1)}^{2}}+{{(1+1)}^{2}}}=\sqrt{8}=2\sqrt{2}\] \[QR=\sqrt{{{(-2\sqrt{3}-1)}^{2}}+{{(\sqrt{3}+1)}^{2}}}=\sqrt{8}=2\sqrt{2}\]Similarly, \[PR=\sqrt{{{(-\,\sqrt{3}-1)}^{2}}+{{(\sqrt{3}-1)}^{2}}}=\sqrt{8}=2\sqrt{2}\]\[\therefore \] \[PQ=QR=PR\] Which shows \[\Delta PQR\] is an equilateral. |
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