Answer:
The coordinates of point C are (b,a).
Step-by-step explanation:
Three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0).
Let the coordinates of point C are (x,y)
We know that the diagonals of a rectangle bisect each other. It means the midpoint of both the diagonals are same.
Midpoint of diagonal AC is
[tex]M=(\frac{0+x}{2},\frac{0+y}{2})=(\frac{x}{2},\frac{y}{2})[/tex]
Midpoint of diagonal BD is
[tex]M=(\frac{0+b}{2},\frac{a+0}{2})=(\frac{b}{2},\frac{a}{2})[/tex]
Equating the midpoint we get
[tex](\frac{x}{2},\frac{y}{2})=(\frac{b}{2},\frac{a}{2})[/tex]
On comparing both the sides, we get
[tex]x=b,y=a[/tex]
Therefore the coordinates of point C are (b,a).
