Question

Show that the points (0, -1), (-2, 3), (6, 7) and (8, 3) are the vertices of a rectangle.

Answer 1

let (0,-1) be x1,y1 , (-2,3) be x2y2 and are as follows for next two

so, by distance formula solve this Q in answer two numbers will be same and other two numbers will be same

Answer 2

Answer:

Given points will form a rectangle.

Step-by-step explanation:

Let's consider

A≡ (0,-1)

B≡ (-2,3)

C≡ (6,7)

D≡ (83)

Now, apply distance formula to find the length of quadrilateral form by these points,

$AB\ =\ \sqrt{(x_2-x_1)^2\ +\ (y_2-y_1))^2}$

 $=\ \sqrt{(-2-0)^2\ +\ (3-(-1))^2}$

     $=\ \sqrt{4\ +\ 16}$

    $=\sqrt{20}$

      $=2\sqrt{5}$

$BC\ =\ \sqrt{(x_3-x_2)^2\ +\ (y_3-y_2))^2}$

     $=\ \sqrt{(6-(-2))^2\ +\ (7-3)^2}$

    $=\ \sqrt{64\ +\ 16}$

   $=\sqrt{80}$

    $=\ 4\sqrt{5}$

$CD\ =\ \sqrt{(x_4-x_3)^2\ +\ (y_4-y_3))^2}$

     $=\ \sqrt{(8-6)^2\ +\ (3-7)^2}$

    $=\ \sqrt{4\ +\ 16 }$

     $=\sqrt{20}$

     $=\ 2\sqrt{5}$

$DA\ =\ \sqrt{(x_1-x_4)^2\ +\ (y_1-y_4))^2}$

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

     $=\ \sqrt{64\ +\ 16}$

    $=\sqrt{80}$

      $=\ 4\sqrt{5}$

So, we can see that

AB = CD

and BC = DA

Hence, the given point will form a rectangle.