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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
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Find the vertices of the square if one of its vertices is (1,1) and the square passes through origin?

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

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1 Answer

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$\therefore$ 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 $m_1\times m_2=-1$
$\large\frac{1}{1}\times \frac{y_1}{x_1}$$=-1$
$y_1=-x_1$
Now $AO=\sqrt 2$,hence $BO=\sqrt 2$
$\sqrt{x_1^2+y_1^2}=\sqrt 2$
$\sqrt {2x_1^2}=\sqrt 2$
$\pm \sqrt{2}x_1=\sqrt 2$
$x_1=\pm 1$
also $y_1=\pm 1$
So $B$ is in the second quadrant hence (-1,1) & D is the fourth quadrant hence (1,-1)
Hence (a) is the correct answer.
answered Feb 4, 2014 by sreemathi.v
 

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