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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

Correct Answer:



C) Equilateral

Description for Correct answer:

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

Comments

Similar Questions

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A). \( \Large \frac{2}{\sqrt{10}} \)

B). \( \Large \frac{4}{\sqrt{10}} \)

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3). If
\( \begin{vmatrix}
x_{1} & y_{1} & 1 \\
x_{2} & y_{2} & 1 \\
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