Given points A(9,0), B(9,6), C(-9,6) and D(-9,0) are the vertices of a quadrilateral. We need to determine whether it is a square, rectangle, rhombus or trapezium.

Rectangle definition:
A rectangle is a quadrilateral in which all four angles are right angles. The opposite sides of a rectangle are parallel and have the same length.

Steps to check if the given quadrilateral is a rectangle:
1. Find the length and breadth of the quadrilateral.
2. Check if opposite sides are parallel.
3. Check if all angles are right angles.

Finding the length and breadth of the quadrilateral:
Length of the quadrilateral AB = 6 – 0 = 6 units
Length of the quadrilateral CD = 0 – 6 = –6 units
Breadth of the quadrilateral BC = –9 – 9 = –18 units
Breadth of the quadrilateral AD = 0 – 0 = 0 units

Checking if opposite sides are parallel:
AB and CD are vertical lines and hence parallel.
BC and AD are horizontal lines and hence parallel.

Checking if all angles are right angles:
Let's find the slopes of AB, BC, CD, and DA.
Slope of AB = (6 – 0) / (9 – 9) = undefined
Slope of BC = (6 – 6) / (–9 – 9) = 0
Slope of CD = (6 – 0) / (–9 – 9) = undefined
Slope of DA = (0 – 0) / (–9 – 9) = 0

AB and CD are vertical lines and hence have undefined slopes. BC and DA have slopes 0. Therefore, AB and CD are perpendicular to BC and DA respectively. Hence, all four angles of the quadrilateral are right angles.

Since the given quadrilateral satisfies all the conditions of a rectangle, it can be concluded that it is a rectangle. Hence, option B is the correct answer.