10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

If three points \[(0,0),\] \[(3,\sqrt{3)}\] and \[(3,\,\lambda )\] form an equilateral triangle, then \[\lambda \] equals:

A) \[2\]

B) \[-3\]

C) \[-4\]

D) None of these

Correct Answer: D

Solution :

[d] Let the given points are \[A(0,0),\] \[B(3,\sqrt{3})\] and \[C(3,\lambda )\]

Since, \[\Delta ABC\]is an equilateral triangle, therefore\[AB=BC\]

\[\sqrt{{{(3-0)}^{2}}+{{(\sqrt{3}-0)}^{2}}}=\sqrt{{{(3-0)}^{2}}+{{(\lambda -0)}^{2}}}\]

\[9+3=9+{{\lambda }^{2}}\]

\[{{\lambda }^{2}}=3\]

\[\lambda =\pm \sqrt{3}\]