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?