Coordinate Geometry Question 45
Question: If the points (1,1) (-1,-1) $ (-\sqrt{3},\sqrt{3}) $ are the vertices of a triangle, then this triangle is
[MP PET 2004]
Options:
A) Equilateral
B) Right-angled
C) Isosceles
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given, vertices of triangle are $ A(1,1),B(-1,-1) $ and $ C(-\sqrt{3},\sqrt{3}) $ Now, $ AB=\sqrt{{{(-1-1)}^{2}}+{{(-1-1)}^{2}}}=\sqrt{4+4}=\sqrt{8} $
$ BC=\sqrt{{{(-\sqrt{3}+1)}^{2}}+{{(\sqrt{3}+1)}^{2}}}=\sqrt{8} $
$ CA=\sqrt{{{(1+\sqrt{3})}^{2}}+{{(1-\sqrt{3})}^{2}}}=\sqrt{8} $ i.e., $ AB=BC=CA $ . So, it is an equilateral triangle.
BETA
