SOLUTION: The coordinates of three vertices of a parallelogram are (−3, 3), (2, 3), and (4, −1). What are the coordinates of the fourth vertex?

Algebra ->  Linear-equations -> SOLUTION: The coordinates of three vertices of a parallelogram are (−3, 3), (2, 3), and (4, −1). What are the coordinates of the fourth vertex?      Log On


   

Question 1153113: The coordinates of three vertices of a parallelogram are (−3, 3), (2, 3), and (4, −1). What are the coordinates of the fourth vertex?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The coordinates of three vertices of a parallelogram are
A(-3, 3), B(2, 3),=> these two points lie on a horizontal line y=3
and C(4, -1), D(x, y)=> since parallelogram,these two points must lie on a horizontal line y=-1
so far we know D(x, -1)
since parallelogram, AB=CD; so, the distance between them is same
find the distance between points A and B
since both points lie on horizontal line, count the number of units between them
d=5
or, you can do it this way:
d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29
d=sqrt%28%282-%28-3%29%29%5E2%2B%283-3%29%5E2%29
d=sqrt%28%282%2B3%29%5E2%2B%280%29%5E2%29
d=sqrt%285%5E2%29
d=5
now, you know the distance, y coordinate, and point C:
d=5,y=-1,
C(4, -1)
D(x, -1)
since point A in quadrant II, point D in quadrant III because AD%7C%7CBC
go from C(4, -1) 5 units from x=4 to the left and you will et to -1
=> the fourth vertex is at D(-1, -1)