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# If the points (1, 1), (-1, 1), $$\left( -\sqrt{3}, \sqrt{3} \right)$$ are the vertices of a triangle, then this triangle is:

 A) right angled B) isoscels C) Equilateral D) none of these

 C) Equilateral

Let $$\Large P \left(1,\ 1\right),\ Q \left(-1,\ -1\right)\ and\ R \left(-\sqrt{3},\ \sqrt{3}\right)$$

$$\Large \triangle PQR$$

Therefore, $$\Large PQ=\sqrt{ \left(1+1\right)^{2}+ \left(1+1\right)^{2} }=\sqrt{8}=2\sqrt{2}$$

$$\Large QR=\sqrt{ \left(-\sqrt{3}+1\right)^{2}+ \left(\sqrt{3}+1\right)^{2} }=\sqrt{8}=2\sqrt{2}$$

Similarly, $$\Large PR=\sqrt{ \left(-\sqrt{3}-1\right)^{2}+ \left(\sqrt{3}-1\right)^{2} }=\sqrt{8}=2\sqrt{2}$$

=> $$\Large PQ - QR = PR$$

Which shows, triangle PQR is an equilateral

Part of solved Rectangular and Cartesian products questions and answers : >> Elementary Mathematics >> Rectangular and Cartesian products

Similar Questions
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