find coord's of square's 4th corner given coord's of other 3

[JayJay06]

May someone help me please?

The question is: ABCD is a square. If the coordinates of three of its vertices are A(-1, 2a), B(a, 2a), C(-a, 0), find the coordinates of D.

 

[soroban]

Re: find coord's of square's 4th corner given coord's of oth

Hello, JayJay06!

Is there a typo? .Could point $\displaystyle A$ be $\displaystyle (-a,2a)$ ?

$\displaystyle ABCD$ is a square.
If the coordinates of three of its vertices are: $\displaystyle A(-a, 2a),\:B(a, 2a),\:C(-a, 0),$
find the coordinates of $\displaystyle D$.

As tkhunny suggested, plot the points.

                |
       (-a,2a)  |   (a,2a)
        A *-----+-----* B
          |     |     |
          |     |     |
          |     |     |
          |     |     |
          |     |     |
    - - C *-----+-----* D - -
       (-a,0)   |   (?,?)

Got any good guesses?

 

[JayJay06]

No, there is no typo. A (-1, 2a) , B (a, 2a) , C (-a 0).

 

[soroban]

Hello, JayJay06!

No, there is no typo. A (-1, 2a) , B (a, 2a) , C (-a 0).

It can still be solved.

           (-1,2a)  |   (a,2a)
            A *-----+-----* B
              |     |     |
              |     |     |
              |     |     |
              |     |     |
              |     |     |
        - - C *-----+-----* D - -
           (-a,0)   |   (?,?)

Since $\displaystyle A(-1,2a)$ and $\displaystyle B(a,2a)$ are horizontally oriented,
then $\displaystyle C(-a,0)$ and $\displaystyle D$ must be horizontal . . . and $\displaystyle D$ is on the x-axis.

Then $\displaystyle C$ must be directly below $\displaystyle A$ . . . This makes: $\displaystyle a = 1$

So we have:

           (-1,2)   |   (1,2)
            A *-----+-----* B
              |     |     |
              |     |     |
              |     |     |
              |     |     |
              |     |     |
        - - C *-----+-----* D - -
           (-1,0)   |   (?,?)

So can you guess where $\displaystyle D$ is?