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

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$=(\frac{a+a}{2},\frac{0+a}{2})=(\frac{2a}{2},\frac{a}{2})=(a,\frac{a}{2})$........(2)

Mid point of AC$=(\frac{0+x}{2},\frac{0+y}{2})=(\frac{x}{2},\frac{y}{2})$......(3)

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

$(\frac{x}{2},\frac{y}{2})=(a,\frac{a}{2})\\\Rightarrow\frac{x}{2}=a;\frac{y}{2}=\frac{a}{2}$

 $\Rightarrow\ x=2a\ and\ y=a$

⇒C=(2a,a)

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

Answer 2

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