Question

The points (0 , -1) , (2 , 1) , (0 , 3) , and (-2 , 1) are the vertices of a

• A. Square
• B. Paralleogram
• C. Rectangle
• D. None of these

Answer 1

Answer: (A)

Square

Let $A(0,-1),B(2,1),C(0,3)$ and $D(-2,1)$

Now we are going to find distance between sides $AB,BC,CD$ and $DA$

$AB=\sqrt{(2-0{)}^2+(1+1{)}^2}=\sqrt{4+4}=\sqrt{8}$

$BC=\sqrt{(0-2{)}^2+(3-1{)}^2}=\sqrt{4+4}=\sqrt{8}$

$CD=\sqrt{(-2+0{)}^2+(1-3{)}^2}=\sqrt{4+4}=\sqrt{8}$

$DA=\sqrt{(0+2{)}^2+(-1-1{)}^2}=\sqrt{4+4}=\sqrt{8}$

$\Rightarrow$ $AB=BC=CD=DA$

Now we are going to find distance between diagonals $AC$ and $BD$

$AC=\sqrt{(0-0{)}^2+(3+1{)}^2}=\sqrt{16}=4$

$BD=\sqrt{(-2-2{)}^2+(1-1{)}^2}=\sqrt{16}=4$

$\Rightarrow$ $AC=BD$

Here, we can see distance between four sides are equal and distance between diagonals are also equal.

$\therefore$ The given points are the vertices of a square.