Question

The centre of a square is at the origin and vertex is $A(2,1)$. Find the co-ordinates of other vertices of the square.

• A. $B(1,-2),C(-2,-1),D(-1,-2)$
  
• B. $B(-1,-2),C(-2,-1),D(-1,-2)$
• C. $B(-1,2),C(-2,-1),D(1,-2)$
• D. $(-1,-2),C(-2,-1),D(1,2)$

Answer 1

The correct option is C $B(-1,2),C(-2,-1),D(1,-2)$

All the sides of a square $ABCD$ are equal

$AB=\sqrt{{(-1-2)}^2+{(2-1)}^2}=\sqrt{9+1}=\sqrt{10}BC=\sqrt{{(-2+1)}^2+{(-1-2)}^2}=\sqrt{1+9}=\sqrt{10}CD=\sqrt{{(1+2)}^2+{(-2+1)}^2}=\sqrt{9+1}=\sqrt{10}AD=\sqrt{{(2-1)}^2+{(1+2)}^2}=\sqrt{1+9}=\sqrt{10}$

Co-ordinates of other vertices of the square $ABCD$ are $B(-1,2),C(-2,-1),D(1,-2)$