Missing coordinate

[jazziza87]

I have a question that gives me three vertices and their coordinates of a square, but tells me to find the coordinates of the last vertex. If someone can give me the method on finding it I would really appreciate :lol:

 

[stapel]

Hint: The sides of a square all have the same length, opposite sides are parallel, and ajacent sides are perpendicular.

Eliz.

Edit: Ne'mind. Answer provided below.

 

[soroban]

Hello, jazziza87!

Did it occur to you to plot the points?
The answer should be obvious . . . almost.

I have a question that gives me three vertices and their coordinates of a square,
but tells me to find the coordinates of the last vertex.

Example \(\displaystyle \;A(2,1),\;B(2,4),\;C(5,4).\;\) Find the fourth vertex \(\displaystyle D\)

      |  (2,4)   (5,4)
      |    B* - - *C
      |     :     :
      |     :     :
      |     :     :
      |    A* - - oD
      |  (2,1)
    --+---------------

Can you even guess the coordinates of \(\displaystyle D\) ?



Example \(\displaystyle \;A(2,1),\;B(0,4),\;C(3,6).\;\) Find the fourth vertex \(\displaystyle D.\)

      |     C
      |     *(3,6)
     B|  *   *
 (0,4)*       *
      |*       *
      | *       oD
      |  *   *
      |  A*
      | (2,1)
    --+-------------

Okay, this one is trickier, but we don't need any fancy formulas.

Opposite sides of a square are parallel, so \(\displaystyle AD\,\parallel\,BC.\)

To go from \(\displaystyle B\) to \(\displaystyle C\), we move: right 3, up 2.

Hence, to go from \(\displaystyle A\) to \(\displaystyle D\), we also move: right 3, up 2.

So, \(\displaystyle D\) must be at \(\displaystyle (5,3).\)