Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
0 votes

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

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

Can you answer this question?

1 Answer

0 votes
$\therefore$ O is the mid point of AC hence $C(x,y)$
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$
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

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App