The diagonals of a rectangle bisect each other.
The coordinate of the point C is (2a, 2b).
What is a rectangle?
A rectangle is a two-dimensional geometrical figure that has two equal and parallel opposite sides and at least one right angle.
It is clear from the diagram of the rectangle, the coordinate of the point C is (2a, 2b).
Let, the midpoint of AC diagonal is O.
Therefore, the 'x-coordinate' of the point O is
[tex]= \frac{2a+0}{2}\\ = a[/tex]
Therefore, the 'y-coordinate' of the point O is
[tex]= \frac{0+2b}{2}\\ = b[/tex]
Therefore, the coordinate of point O is (a, b).
Let, the midpoint of BD diagonal is P.
Therefore, the 'x-coordinate' of the point P is
[tex]= \frac{2a+0}{2}\\ = a[/tex]
Therefore, the 'y-coordinate' of the point P is
[tex]= \frac{0+2b}{2}\\ = b[/tex]
Therefore, the coordinate of point P is (a, b).
Therefore, P and O are same point.
Hence, the diagonals of the rectangle bisect each other.
Learn more about a rectangle here:
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