Question

Examine whether the following points taken in order form a rectangle.

(-1, 1), (0, 0), (3, 3) and (2, 4)

Answer 1

Let us consider the given points as $A(-1,1);B(0,0);C(3,3);D(2,4)$.

The distance between $AB=\sqrt{(-1-0{)}^2+(1-0{)}^2}=\sqrt{1+1}=\sqrt{2}$

The distance between $BC=\sqrt{(0-3{)}^2+(0-3{)}^2}=\sqrt{9+9}=\sqrt{18}$

The distance between $CD=\sqrt{(3-2{)}^2+(3-4{)}^2}=\sqrt{1+1}=\sqrt{2}$

The distance between $DA=\sqrt{(2+1{)}^2+(4-1{)}^2}=\sqrt{9+9}=\sqrt{18}$

The distance between $AC=\sqrt{(-1-3{)}^2+(1-3{)}^2}=\sqrt{(-4{)}^2+(-2{)}^2}=\sqrt{16+4}=\sqrt{20}$

The distance between $BD=\sqrt{(0-2{)}^2+(0-4{)}^2}=\sqrt{4+16}=\sqrt{20}$

As the opposite sides $AB=CD$ and $BC=DA$ and the diagonals $AC=BD$.

Therefore, the quadrilateral which is formed by the points $A,B,C,D$ is a rectangle.

Hence, this is the answer.