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# solve- if one vertex of an equilateral triangle of side "a" lies at origin and other lies on the line x=(square root of 3)*y the third vertex is..

Jitender Singh IIT Delhi
7 years ago
Ans: y-axis
Sol:
First vertex lie at the origin O (0, 0). The second vertex A lie on th line
$y = \frac{1}{\sqrt{3}}x$
Slope of this line is 30 & portion of length ‘a’ of this line is one side of tringle OAB. So the slope of one other side should be 90 as angle b/w sides of OAB should be 60. So the third vertex should lie on this sides which is y-axis. We have
$B (\frac{\sqrt{3}a}{2}, \frac{a}{2})$
$C (0, a)$
Thanks & Regards
Jitender Singh
IIT Delhi