SOLUTION: these are the corrdinates of three points (0,10),(30,10),(20,-30) find a fourth point so that the four points form the vertices of a parallelogram. how would you do this? how

Question 118474: these are the corrdinates of three points (0,10),(30,10),(20,-30)
find a fourth point so that the four points form the vertices of a parallelogram.
how would you do this? how many different points could be the fourth vertex?what are the coordinates of these points? write your answers below. show the different possible parallelograms in different colors on the grid.
Luke and his mom..
Answer by scott8148(5883) (Show Source):
You can put this solution on YOUR website!
if you draw a triangle, using the three points as the vertices,
___ you can visualize two sides of the triangle as sides of a parallelogram
___ and the third side of the triangle as a diagonal of the parallelogram

since there are 3 possible diagonals, there are 3 possible parallelograms
___ remember, the diagonals of a parallelogram bisect each other
___ (they cross at their midpoints)

let the first two points form a diagonal
___ the midpoint is ((0+30)/2,(10+10)/2) or (15,10)
___ this is also the midpoint of the other diagonal
let (x,y) be the missing vertex
___ so (x+20)/2=15 and (y-30)/2=10
___ x=10 and y=50 ___ the missing vertex is (10,50)

you can repeat this for the other 2 "diagonals"