Question

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)

Answer 1

(2a,a)
is ur answer
hope this helps

Answer 2

Answer:-(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
`=((a+a)/(2),(0+a)/(2))=((2a)/(2),(a)/(2))=(a,(a)/(2))`........(2)

Mid point of AC
`=((0+x)/(2),(0+y)/(2))=((x)/(2),(y)/(2))`......(3)

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

`((x)/(2),(y)/(2))=(a,(a)/(2))\\\Rightarrow(x)/(2)=a;(y)/(2)=(a)/(2)`

`\Rightarrow\ x=2a\ and\ y=a`

⇒C=(2a,a)

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