James is writing a coordinate proof involving a parallelogram. knowing that the opposite sides of a parallelogram are congruent, james places his parallelogram on the coordinate plane such that one vertex is at the origin and one side lies along the x-axis. what coordinates should he assign to the fourth vertex of the parallelogram? (2a, a) (2a, a2) (a2, 0) (2a, 2a) 

-(2a,a) coordinates he should assign to the fourth vertex of the parallelogram.

Explanation:-

Let ABCD be the vertices of the given parallelogram such that A=(0.,0) , B=(a,0) , C(x,y) and D=(a,a)

Construct the diagonals AC and BD of parallelogram ABCD .

We know that diagonals of a parallelogram bisect each other.

⇒ mid point of AC= mid point of BD...(1)

Mid point of BD........(2)

Mid point of AC......(3)

Substitute (2) and (3) in (1), we get

⇒C=(2a,a)

⇒ (2a,a) coordinates he should assign to the fourth vertex of the parallelogram.

answer: 4 (:

step-by-step explanation: