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The center of a square is at the origin ...

The center of a square is at the origin and its one vertex is `A(2,1)dot` Find the coordinates of the other vertices of the square.

Text Solution

Verified by Experts

The correct Answer is:
(-2,1), (-1,2) and (1,-2)

ABCD is square having centre at origin.
Clearly, `C-=(-2,-1)`
`AO = sqrt(5)`
`"Slope of AO" = (1-0)/(2-0) = (1)/(2)`
`therefore " Slope of BD" =-2`
`rArr -2="tan" theta`
`therefore " cos" theta=-(1)/(sqrt(5)) " and sin" theta = (2)/(sqrt(5))`
Since B and D are on BD at a distance `sqrt(5)` from O, their coordinates (in some order) will be
`(0+-sqrt(5) "cos" theta, 0+-sqrt(5) "sin" theta)`
`(0overset(-)(+)1,0 +-2)`
or (-1,2 and (1,-2)
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