# Find the vertices of the square if one of its vertices is (1,1) and the square passes through origin?

$\begin{array}{1 1}(a)\;B(-1,1),C(-1,-1),D(1,-1)&(b)\;B(1,1),C(1,-1),D(-1,1)\\(c)\;B(1,1),C(-1,1),D(1,1)&(d)\;B(-1,1),C(-1,-1),D(-1,-1)\end{array}$

$\therefore$ O is the mid point of AC hence $C(x,y)$
$0=\large\frac{1+x}{2}$
$x=-1$
$0=\large\frac{1+y}{2}$
$y=-1$
Hence $C(-1,-1)$
Now $B(x_1,y_1)$
$AO\perp BO$
Hence $m_1\times m_2=-1$