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 \(\displaystyle D\)
Code:
| (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 \(\displaystyle D.\)
Code:
| 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 \(\displaystyle (5,3).\)