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

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

Suppose I'm given $2D$ coordinates of two opposite vertices $B$ and $D$ of an $ABCD$ rectangle. And I know the coordinate of the intersection point $O$ of the diagonals $AC$ and $BD$ of that rectangle.

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

2. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

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.

3. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

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

4. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

Hello, x3bnm!

Suppose I'm given coordinates of two opposite vertices $B$ and $D$ of an $ABCD$ rectangle.
And I know the coordinate of the intersection point $O$ of the diagonals $AC$ and $BD$ of that rectangle.

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

Code:
              * * *
*           *  A
*               o
*                 *

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

*                 *
o                *
C  *           *
* * *
Let $BD$ be the diameter of a circle.
Then vertex $A$ can be any point on one semicircle.
(And $C$ is diametrically opposite $A.$)

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

5. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

Originally Posted by Soroban
Hello, x3bnm!

Code:
              * * *
*           *  A
*               o
*                 *

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

*                 *
o                *
C  *           *
* * *
Let $BD$ be the diameter of a circle.
Then vertex $A$ can be any point on one semicircle.
(And $C$ is diametrically opposite $A.$)

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 $X$ and $Y$ 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?

6. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

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?

7. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

Hello, x3bnm!

$\text{Yes, the rectangle I'm talking about has sides parallel to }x\text{- and }y\text{-axes.}$

Did you take richard1234's suggestion?

Suppose the coordinate are: . $B(p,q),\;D(r,s)$

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 $r-p$ and the height is $q-s.$

8. ## Re: Find the area of a rectangle:Given coordinates of centroid and 1 pair opposite po

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

Suppose there is a $ABCD$ rectangle(sides are parallel to $X$ and $Y$ axis) where the coordinates of opposite vertices $B$ is $(1,1)$ and the coordinates of $D$ is $(4,3)$.

We can easily get the coordinates of $A$ as $(1,3)$ and $B$ as $(4,1)$.

Now it will be easy to calculate the area of rectangle because you have the coordinates of all $4$ vertices.

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