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 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :
Solutions · 1
Official solution
Let, coordinate of point A = (x, y).
\[\therefore\,\,\,\] For point A,
\[{x \over {\cos {{30}^ \circ }}}\] = \[{y \over {\sin {{30}^ \circ }}}\] = 2
\[ \Rightarrow \] x = \[\sqrt 3 \]
and y = 1
Similarly, For point B,
\[{x \over {\cos {{75}^ \circ }}}\] = \[{y \over {\sin {{75}^ \circ }}}\] = 2\[\sqrt 2 \]
\[\therefore\,\,\,\] x = \[\sqrt 3 - 1\]
y = \[\sqrt 3 + 1\]
For point C,
\[{x \over {cos{{120}^ \circ }}}\] = \[{y \over {sin{{120}^ \circ }}}\] = 2
\[ \Rightarrow \] x =−1
y =3\therefore\,\,\,\[ Sum of the x - coordinate of the vertices
= 0 + \]\sqrt 3 +3−1 + (−1) = 23−