Question

The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?

Answer 1

Answer:

only one cordinate ( 1 , - 2)

x = 1   , y = -2

Step-by-step explanation:

The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1)

Let say Forth vertex coordinate = (x , y)

AB ║ CD

=> Slope are equal

=>  (3 - 0)/(4 - 2)  = (y - 1)/(x - 3)

=> 3(x - 3) = 2(y - 1)

=> 3x - 9 = 2y - 2

=> 3x - 2y = 7

AD ║ BC

=> (1-3)/(3-4) = (y - 0)/(x - 2)

=> -2x + 4 = -y

=> 2x - y  = 4

=> 4x - 2y = 8

Subtracting 1st

=> x = 1   , y = -2

only one cordinate is possible