JEE Main 2017 (Online) 9th AprilQuestion 1
A square, of each side $2$, lies above the $x$-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle $30^\circ$ with the positive direction of the $x$-axis, then the sum of the $x$-coordinates of the vertices of the square is :
Points and Straight Lines
Solution
Vertices: $(0,0)$, $(\sqrt3,1)$, $(-1,\sqrt3)$, $(\sqrt3-1,\sqrt3+1)$; sum of $x$-coordinates $=2\sqrt3-2$.