Vertices of a parallelogram question

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gohoyas

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Hello Happy New Year to all!

I need assistance with the following 2 questions please:

Points A (-3,-1), B (-1,1) and C (1,1) are three vertices of a parellelogram.

1) How may parallelograms can be formed using the three points?

2) Give the coordinates of the fourth vertex of the other parallelogram?
 
Well, \(\displaystyle \overline{BC} = \overline{AD}\) and \(\displaystyle \overline{BA} = \overline{CD}\). This certainly narrows the choices for the fourth point.
 
gohoyas said:
Hello Happy New Year to all!

I need assistance with the following 2 questions please:

Points A (-3,-1), B (-1,1) and C (1,1) are three vertices of a parellelogram.

1) How may parallelograms can be formed using the three points?

2) Give the coordinates of the fourth vertex of the other parallelogram?
Click to expand...

Plot the points on a graph paper - and stare at it a bit. Answer will become very clear....

Each of the lines (AB, BC and CD) could become diagonals of a parallelogram. And think more......

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.
 
Last edited by a moderator:
Hello, gohoyas!

I don't suppose you made any sketches . . .

\(\displaystyle \text{Points }A (\text{-}3,\text{-}1),\;B (\text{-}1,1),\;C (1,1)\text{ are three vertices of a parellelogram.}\)

\(\displaystyle \text{1) How many parallelograms can be formed using the three points?}\)

\(\displaystyle \text{2) Give the coordinates of the fourth vertex of the other parallelograms?}\)
Click to expand...

We are given these three points.

Code: 
                        |
                    B   |   C
              (-1,1)o * * * o(1,1)
                  *     *
      - - - - - * - * - + - - - - - -
              * *       |
     (-3,-1)o           |
            A           |


There are three possible locations for vertex \(\displaystyle D.\)

Code: 
. . .               |           D
. . .               |           ♥(3,3)
. . .               |       * *
. . .               |   *   *
. . .          B    *     *
. . .           o   |   o
. . .         *     *    C
      - - - * - * - + - - - - - - -
          * *       |
        o           |
        A           |


Code: 
                            |
                       B    |    C
                        o * * * o
                    *       *
      - - - - - * - . - * - + - - -. - -
            *       *       |
      D ♥ * * * o           |
     (-5,-1)     A           |
                            |


Code: 
                    |
               B    |    C
                o * * * o
              *     | *
      - - - * - * - + - - - -
          *       * |
        o * * * ♥ D |
       A     (-3,-1)|
 
You must have mistyped the coordinates for the third case; you must have meant ♥D (-1, -1) as opposed to ♥D(-3,-1).

Cheers,
Sai.


soroban said:
Hello, gohoyas!

I don't suppose you made any sketches . . .


We are given these three points.

Code: 
                        |
                    B   |   C
              (-1,1)o * * * o(1,1)
                  *     *
      - - - - - * - * - + - - - - - -
              * *       |
     (-3,-1)o           |
            A           |


There are three possible locations for vertex \(\displaystyle D.\)

Code: 
. . .               |           D
. . .               |           ♥(3,3)
. . .               |       * *
. . .               |   *   *
. . .          B    *     *
. . .           o   |   o
. . .         *     *    C
      - - - * - * - + - - - - - - -
          * *       |
        o           |
        A           |


Code: 
                            |
                       B    |    C
                        o * * * o
                    *       *
      - - - - - * - . - * - + - - -. - -
            *       *       |
      D ♥ * * * o           |
     (-5,-1)     A           |
                            |


Code: 
                    |
               B    |    C
                o * * * o
              *     | *
      - - - * - * - + - - - -
          *       * |
        o * * * ♥ D |
       A     (-3,-1)|
Click to expand...
 
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