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[tex]=(\frac{a+a}{2},\frac{0+a}{2})=(\frac{2a}{2},\frac{a}{2})=(a,\frac{a}{2})[/tex]........(2)
Mid point of AC[tex]=(\frac{0+x}{2},\frac{0+y}{2})=(\frac{x}{2},\frac{y}{2})[/tex]......(3)
Substitute (2) and (3) in (1), we get
[tex](\frac{x}{2},\frac{y}{2})=(a,\frac{a}{2})\\\Rightarrow\frac{x}{2}=a;\frac{y}{2}=\frac{a}{2}[/tex]
[tex]\Rightarrow\ x=2a\ and\ y=a[/tex]
⇒C=(2a,a)
⇒ (2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
