Thread: parallelogram

Three vertices of a parallelogram are (1,1), (3,5), and (-1,4) . find all possible ordered pairs that could be the coordinates of the fourth vertex .

(-3,0), (5,2), (1,8)

Hello, sri340!

Three vertices of a parallelogram are: A(1,1), B(3,5), and C(-1,4).
Find all possible ordered pairs that could be the coordinates of the fourth vertex .

This can be solved without any fancy formulas . . .

Code:

          |           B
          |         (3,5)
          |           o
          |     *    *  *
    C     *         *     *
    o     |        *        *
(-1,4)*   |       *           *
        * |      *              o D
          *     *         *
          | *  *    *
          |   o
          | (1,1)
          |   A
- - - - - + - - - - - - - - - - - - -
          |

Suppose vertex is to the right, as shown in the diagram.

Going from to , we move: right 4, up 1.

Since , going from to , we make the same moves.

Therefore: .


There are two more possible locations for vertex :
. . left and above , and left and below