Question

In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C?

Answer 1

What are the coordinates of point C are (b,a)

Answer 2

The coordinates of point C are (b,a).

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

`M=((0+x)/(2),(0+y)/(2))=((x)/(2),(y)/(2))`

Midpoint of diagonal BD is

`M=((0+b)/(2),(a+0)/(2))=((b)/(2),(a)/(2))`

Equating the midpoint we get

`((x)/(2),(y)/(2))=((b)/(2),(a)/(2))`

On comparing both the sides, we get

`x=b,y=a`

Therefore the coordinates of point C are (b,a).