Thread: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite points

Suppose I'm given coordinates of two opposite vertices and of an rectangle. And I know the coordinate of the intersection point of the diagonals and of that rectangle.

Is it possible to find the area of the rectangle using this information? If yes what is the procedure for that?

No. It's like saying, you're given the length of the hypotenuse of a right triangle. You cannot determine the legs of the triangle given only the hypotenuse.

Thanks richard1234. That's all I wanted to know. I've to find another way to compute the area. Again thanks.

Hello, x3bnm!

Suppose I'm given coordinates of two opposite vertices and of an rectangle.
And I know the coordinate of the intersection point of the diagonals and of that rectangle.

Is it possible to find the area of the rectangle using this information?
If yes, what is the procedure for that?

With no more information, richard1234 is correct.

Code:

              * * *
          *           *  A
        *               o
       *                 *

      *                   *
    B o - - - - * - - - - o D
      *         O         *

       *                 *
        o                *
       C  *           *
              * * *

Let be the diameter of a circle.
Then vertex can be any point on one semicircle.
(And is diametrically opposite )

If the sides of the rectangle are parallel to the coordinate axes,
. . then a unique solution is possible.

Originally Posted by Soroban

Hello, x3bnm!


With no more information, richard1234 is correct.

Code:

              * * *
          *           *  A
        *               o
       *                 *

      *                   *
    B o - - - - * - - - - o D
      *         O         *

       *                 *
        o                *
       C  *           *
              * * *

Let be the diameter of a circle.
Then vertex can be any point on one semicircle.
(And is diametrically opposite )

If the sides of the rectangle are parallel to the coordinate axes,
. . then a unique solution is possible.

Yes the rectangle I'm talking about has sides parallel to and axis.

In that case how can I calculate the area of the rectangle if I'm given only coordinates of 1 pair of opposite vertices of the rectangle and the centroid?

If you know that the opposite vertices are (a,b) and (c,d), and that the sides are parallel to the x- and y-axes. Draw the rectangle first. What are the lengths of the base and height?

Hello, x3bnm!

Did you take richard1234's suggestion?

Suppose the coordinate are: .

Plot the two vertices.

Code:

      |       B
      |       *
      |     (p,q)
      |
      |                   D
      |                   *
      |                 (r,s)
      |
  - - + - - - - - - - - - - - -
      |

You can see the rectangle, can't you?

Code:

      |
      |     (p,q)
    q *     B * - - - - - * C
      |       :           :
      |       :           :
      |       :           :
    s *     A * - - - - - * D
      |                 (r,s)
      |
  - - + - - - * - - - - - * - -
      |       p           r

And you can see that the width is and the height is

I found the solution to my problem. For those who are interested read on:

Suppose there is a rectangle(sides are parallel to and axis) where the coordinates of opposite vertices is and the coordinates of is .

We can easily get the coordinates of as and as .

Now it will be easy to calculate the area of rectangle because you have the coordinates of all vertices.

Thank you richard1234 and Soroban for your help. I really appreciate your help.